Effects of jet inclination angle and geometrical parameters on air curtain performance.
Tilted air plane jets can be used as dynamic barriers to control and ensure invisible separation between two environments. Quality control and conditions of the environments including temperature, contaminants, pressure and humidity can be maintained independently upon the provision of the specific parameters that will allow the maintenance of the integrity of the air plane jets.
The performance of this dynamic non-physical barrier will be under continuous threat of fluctuating due to the easy existence of perturbation that could result from a change in the various conditions of thermal and pressure conditions on one side of the environment, or from the intrusions of personnel, hands or insects resulting in breaking the integrity of the barrier and requirement of further periods of time to rebuild the jet coupled with consequences of such broken integrity.
The complexity of maintaining the quality and condition of one environment from changes due to influence of another adjacent environment necessitates identification of the combination of factors and in specific the angle causing the tilt of the air jet, that affect the optimal performance of the tilted air jet separating the two environments. Such maintenance is managed upon the consideration of the dynamic nature, the balance between the jet momentum flux and the pressure difference between the two environments, surface stresses, infiltration, entrainment, turbulence generation, internal interactions, physical obstruction by objects and people and nature of work space.
A typical application of the tilted air jet plane is being used in refrigerated display cabinets that exist practically in any commercial outlet, supermarket or mall. Air curtain is used, as a replacement of a see- through glass door. Surveys indicated that such rigid glass door may affect the propensity of the consumers to pick goods from the display cabinet. With the continuous increase of energy cost, the generation of suitable refrigerated environment became a concern for owners in specific when such environment is not protected well against the infiltration of the opposite side of the curtain environment which is usually at different temperature and humidity conditions. If infiltration rate accounts for 70%-80% of a typical case cooling load and if the refrigeration accounts for 50% of typical store electric load, then efforts should be undertaken to minimize the infiltration rate aiming at reducing the energy cost.
Having identified the need for the tools which enable identification of the performance of a tilted air jet, the objective of this present work is to develop a model-based design methodology for the establishment of tilted air jet plane, that will facilitate the design and or evaluate existing designs and in particular the effects of the inclination angle of the jet on the performance of the air curtain.
Air jet planes can be vertical, horizontal or tilted and were introduced for the first time in year 1916. Function and tightness studies were performed in the last 40 years and mainly concentrated on the vertical and horizontal types. Under several titles, air jet planes were immensely considered in research work in both domains: experimental and computational. Some were successful in addressing those parameters that have significant impact on the performance of the jet. Identification of those parameters and quantification allowed some how the determination of certain rates like infiltration and or entrainment expressions.
Many have contributed in developing a number of mathematical models to aid in the design and performance prediction of the air jets. Explicit method was employed to solve the differential equations describing the flow and to prove that the performance of the air jet can be simulated effectively using the finite difference technique; Hetsroni and Hayes, (1).
Finite element method as well as other several patents were taken out on open protection devices with few investigations have been reported; M. Havet et al. (2), who made the study on an air curtain used as a dynamic barrier to separate two environments indicated that the curtain is strongly sensitive to perturbations such as draughts. Studies taking into consideration all major parameters affecting the air curtain flow field by the utilization of modern analytical, computational and experimental techniques, were done by H. Navaz et al. (3), by Brandon S. Field, Eric Loth, (4) and by M. Amin, et al. (5), on the entrainment of ambient air on vertical air curtain upon varying the Reynolds numbers (4200-8000) and the Richardson Number (013-0.58) which again showed that the entrainment of the ambient air was governed by variety of eddy engulfing structures. Also, a numerical simulation was utilized on the two dimensional solution of a vertical down ward-blowing plane jet, J.J Costa et al. (6), and on the flow and heat transfer characteristics of vertical air curtain in a vertical display cabinet with a two--fluid turbulence model; K-Z Yuet al. (7).
However, many experimental works were done on the air jet with little on tilted angle in comparison with the horizontal and vertical air barriers. Works indicated that a breaking point for air curtains occurs if the deflection modulus is below the minimum value for the particular air curtain configuration and the initial turbulence intensity has a moderate effect on the rate of heat transfer through the curtain; Howel reports, (8), (9). Another experiment showed that the mass entrainment rate, dominated by eddy engulfment of ambient air, was directly proportional to the air speed of a down ward vertical blowing isothermal wall jet at moderate Reynolds Numbers (1500-8500) with significant inflow turbulence; B. S. Field & E.Loth, (10).
Experiments on vertical air curtains were more popular. The implication of changing several parameters like ambient air temperature, indoor relative humidity, ambient air flow, Air supply velocity, air flow from back panel and night covers on the performance of the refrigerated display cabinet was identified; Y-G Chen, X-L Yuan, (11). Also, H. K. Navaz et al. (12), carried an investigation on the Jet entrainment in air curtain of open refrigerated display cases where certain parameters like turbulent intensity, shape of the mean velocity profile at the discharge air grille, and the Reynolds Number were identified, quantified and the amount of entrained air was computed and showed that the shape of the vertical velocity profile and the turbulence intensity present at the supply air grille controlled the entrainment rate and at different stages. Plane air jets were experimentally studied as well by K. Loubier, M. Pavageau, (13) using PIV with an emphasis put on the flow structure in the impingement region of jet systems.
Experimental results were not always in conformity with previous works as it was the case with the findings of I. Gray, P. Luscombe et al. (14) when describing that need of having only 70% of total air delivery in circulation needs through air curtain and the balance through side discharge.
The correlation of the numerical solutions with the experimental works results were limited and in specific when using the Computational Fluid Dynamics (CFD) technique. An apparent conflict was demonstrated upon lowering the Reynolds Number aiming at minimizing the air entrainment in a vertical air curtain with the risk of loosing the integrity of the air curtain structure; H. K. Navaz, et al. (15). CFD predictions on infiltration were shown to vary with time limiting the possibility of utilizing the analytical models; A.M. Foster, et al. (16).
CFD modeling which was used to aid the design of retail display cabinets provided a rapid means to understand air flows, optimum jet velocity and their effect on surrounding temperatures; A. M. Foster et al. (17).
From the above review, it was concluded that the effect of jet inclination on the performance of air curtain was not well considered, thus opening areas for attracting further investigation.
To overcome the difficulty in getting the unreliable results in data collected from an experimental set up, this research describes the several experimental and numerical tools that are used in analyzing and assessing the performance of the tilted air jet plane. Making use of Computer Fluid Dynamics (CFD) and its code (18), will contribute to savings in terms of both time and money, and such experiments can be performed for a final check of the correctness of numerical results.
Experimental Set-Up Model
Experimental studies were carried out on a refrigerated display vertical cabinet with internal dimension of D x W x H = 0.6 m x 1.8 m x 1.9 m. This cabinet was located in laboratory facilities at a University's research laboratory in a room of 10 m x 10 m x 4 m with its back side to one of the walls.
The modular simple display case composed of supply air grille with minimum width of 4 cms, and return air grille positioned at variable angles and the air in the room is allowed to mix with the supply incoming air from the jet along the length of the Discharge Air Grille, DAG and along its height. The domain is bounded by two surfaces on the width of the Discharge Air grille, DAG and the Return Air Grille, RAG. The back panel of the display cabinet was perforated to allow theoretically, when goods stored on shelves are not in close proximity of the back panel, cooling for rear products and also to support the flow of vertical air curtain to ensure better performance. Many tests were carried with practically sealed perforation (0%-5%) when noting that most of the display cabinets when used, are fully packed on their shelves and obstructing the flow of air from the back panels.
In a display cabinet, air is drawn through a linear grille at the base of the opening and fans then force it through the cooling coil situated underneath the load volume. The cooled air is forced to a supply plenum located behind the compartment. A fraction of the air is sometimes fed into the unit through perforated plate at the back of the cabinet, while the remaining quantity of the cold air is blown through the Discharge Air Grille, DAG forming the tilted jet plane.
Figure 1 shows a typical vertical display cabinet where the spillage and entrained air portions determine the mass of air returning to the Return Air Grille, RAG.
[FIGURE 1 OMITTED]
Where in Figure 2, the Tilt Angle ([alpha]) and the discharge angle ([alpha]) are shown with variation to either the positive or negative sides.
[FIGURE 2 OMITTED]
The main aim of experiments was to detect the velocity uniformity at the start of the curtain flow and how the integrity of the curtain is affected by entrainment. The experimental results not only provide necessary boundary conditions for later calculation, but also supply data that will be later compared with the results of simulation to assess the accuracy and viability of the established CFD model.
Due to the irregularities of the flow, a more or less significant amount of ambient air is always entrained, reducing the temperature control capabilities and increasing the energy consumption.
The data acquisition systems included temperature acquisition system equipped with special grade T thermocouples a a accurate +/- 0.1[degrees]C, a relative humidity reader accurate to +/-3%, flow meters.
The set up of thermocouples in the experiment were varied in positions to allow more coverage in readings. The sampling interval is 2 seconds. A continuous colored smoke-wire technique has been developed for flow visualization. The improved contrast of colored smoke sheet facilitates flow visualization where a vertical smoke-wire is used for introducing controlled sheets of smoke streaklines while running the cabinet fan. Regulated drops of a mixture of paraffin oil with colored dye are allowed to fall along the stainless steel wire. The wire is thus coated with a thin film of falling paraffin or with minute colored droplets along the length. The oil mixture subsequently evaporates through the resistive heating of the wire thus producing a sheet of colored streaklines. The visualization provided a good insight over the shape of the steady state of the built up curtain. The known directions are prerequisite to effective measurements with the flow meters in the direction of the flow at the inlet.
The variations in the geometrical set up are carried by:
1. Model the fluid flow inside the plenum and all back panel ductwork.
2. Make sure the velocity profile that is obtained from this model is similar to the experimental data that is taken outside the Discharge Air Grille, DAG.
3. Make changes to the Discharge Air Grille, DAG geometry by running the simulation through all the ductworks and obtain the vertical velocity profile at the DAG exit plane.
4. Identify those velocity profiles that resemble a parabola and possess only one peak
5. Identify the velocity profile that is the closest to a skewed parabola shifted towards the inside of the display case.
6. Use the most promising velocity profiles obtained in steps 4 and 5 as a boundary conditions for the flow outside the display case to measure the entrainment rate.
7. Vary the turbulence intensity at the DAG for these velocity profiles to identify its implication on infiltration.
Data obtained were recorded with shown samples at different flow rates (Table 1).
Table 1. Sample of Data Collected # Motor Input Supply Return Average Average Frequency, Average Average Supply Return Hz Airflow Airflow Temperature, Temperature, Rate, m/s Rate, m/s [degrees]C [degrees]C 1 60 3.2 2.6 2.5 7.5 2 50 2.7 2.1 2.5 9.5 3 40 2.3 1.9 2.5 8.9 4 30 1.7 1.5 2.5 8.3 # Ambient Supply Supply to Ambient Cabinet Temperature, Tilt Return Relative Relative [degrees]C Angle, Angle, Humidity, % Humidity, % [degrees] [degrees] 1 20 10 0 51 51 2 20 10 0 51 51 3 20 10 0 51 51 4 20 10 0 51 51 # Average Cabinet Temperature, [degrees]C (Sensors Located on Shelves) 1 5.8 2 4.8 3 5.9 4 7.3 # % of Back Panel Opened Slots, 0%-5% 1 5 2 5 3 5 4 5
The amount of infiltrated air can be related to the temperature of the outside air [T.sub.room], Discharge Air temperature, Temperature of the discharged air in the cabinet, T and the average temperature of the spilled air, where also the amount of spillage air can be related to the average temperature of the spilled air, the temperature of the outside air [T.sub.room] Discharge Air temperature and Temperature of the discharged air in the cabinet, H.K. Navaz, et al. (19).
Results obtained were compared to the particular case study results done by H.K. Navaz, et al. (20), on a specially built air curtain using [CO.sub.2] as one environment. In spite of the difference in the equipment used in the experiments, there was deviation not exceeding 7% upon comparing the meshing done by this study with data provided.
A numerical model is presented to assist in the design of the tilted air jet plane, it allows the calculation of the Infiltration rate based on the assuming levels of mass concentration of [CO.sub.2] available in the Discharge Air Grille, DAG and in the Return Air Grille, DAG. In considering a control volume of the discharge, return, spillage and entrained air,
(m-Infilt.) * Concentration of DAG + Infilt *(Concentration of Env.2) = m * Concentration of RAG Infiltration Rate (C) dimensionless = Infilt./m = [[[DAG] - [RAG]]/[[DAG] - [ENVIRON * 2]]] (1)
where Infilt. is the mass of infiltrated air, C is the infiltration rate, m is the total discharge mass (with zero back panel slots, and [quantities defining concentrations of [CO.sub.2] at specific locations] are in [CO.sub.2] mass concentrations. Similar results were obtained by Faramarzi, R. et al. (21), and Amin, M. et al (22).
This rate is caused by entrainment, inclination of the jet or the momentum to transverse forces and very much by the stack effect which is created by differences in air densities on the two environment sides and resulting in a linear variation in pressure, as described by Hayes & Stoecker, 1969, (23), along the jet. This is carried by calibrating the two-dimensional CFD code.
The availability of the software has remarkably increased the capability of the computation of the air flow pattern and in particular using the finite volume method and the sequential procedure which are employed to discretise and solve the governing differential equations, based on the stream function--vorticity formulation.
Simulation was carried by varying the various parameters including the flow rates and keeping the interest in maintaining an unbroken air curtain.
The mixing of the conditioned jet with the still ambient air is dependent on variables such as the length of the mixing region, initial velocity, temperature, and moisture content distributions and initial turbulence intensity. For vertical display cabinet air curtains, the length to width ratio will, in most cases, be large to accommodate larger space for storing goods. It is assumed that the developed model assumes a well-designed curtain with a low turbulence intensity at the discharge air grille and of 1%.
The turbulent mixing process in air curtains can be described using the Navier--Stokes equations of motion for a Newtonian fluid.
[[[partial derivative]U]/[[partial derivative]x]] + [[[partial derivative]V]/[[partial derivative]y]] = 0 (2)
U[[[partial derivative]U]/[[partial derivative]x]] + V[[[partial derivative]V]/[[partial derivative]y]] = [1/[rho]][[partial derivative]/[[partial derivative]y]](AT[[partial derivative]U]/[[partial derivative]y]) (3)
U[[[partial derivative]T]/[[partial derivative]x]] + V[[[partial derivative]T]/[[partial derivative]y]] = [1/[rho]][[partial derivative]/[[partial derivative]y]](Aq[[partial derivative]T]/[[partial derivative]y]) (4)
U[[[partial derivative]C]/[[partial derivative]x]] + V[[[partial derivative]C]/[[partial derivative]y]] = [1/[rho]][[partial derivative]/[[partial derivative]y]]([rho]D[[partial derivative]C]/[[partial derivative]y]) (5)
Set of mathematical governing equations was used to describe the two-dimensional steady-state flow of the turbulent buoyant air curtain. The Turbulence model was taken as k-[epsilon] model, pressure based implicit to ensure stability and steady conditions. The two equations Model was considered without any change in their default constants as lacking other accurate information.
k denotes the kinetic turbulent energy and [epsilon] represents the rate of dissipation of turbulent kinetic energy. The buoyancy-revised k-[epsilon] model was able to evaluate their values:
[rho]([[partial derivative]k]/[[partial derivative]t] + U[[partial derivative]k]/[[partial derivative]x]) = [[partial derivative]/[[partial derivative]x]]([mu] + [rho][upsilon]/[[sigma]k])[[[partial derivative]k]/[[partial derivative]x]] + [rho][upsilon]([[partial derivative]U]/[[partial derivative]x] + [[partial derivative]V]/[[partial derivative]x])[[[partial derivative]U]/[[partial derivative]x]] + u[rho]'g - [rho][epsilon] (6)
[rho]([[partial derivative][epsilon]]/[[partial derivative]t] + U[[partial derivative][epsilon]]/[[partial derivative]x]) = [[partial derivative]/[[partial derivative]x]]([mu] + [rho][upsilon]/[[sigma][epsilon]])[[[partial derivative][epsilon]]/[[partial derivative]x]] + c[epsilon][rho][upsilon][[epsilon]/k]([[partial derivative]U]/[[partial derivative]x] + [[partial derivative]V]/[[partial derivative]x])[[[partial derivative]U]/[[partial derivative]x]] - c[epsilon][[[epsilon]2]/k] (7)
To obtain a final solution for the velocity, the above set of partial equations were used for computing the distribution of velocity for the turbulent air flow simultaneously and iteratively until the boundary conditions are satisfied within a specified degree of convergence illustrated by 2 [e.sup.-5]. Boundary conditions were set for individual parameter, the discharge air grille, DAG by defining the direction specification method as Normal to Boundary with 2.5% turbulent intensity and turbulence length of scale of 0.04 m. For the pressure inlet, it was set at turbulent intensity of 0.1 and turbulence length of scale of 0.5 m.
The room air flow pattern was assumed to have a pressure inlet resulting from the flow at the discharge air grille, DAG and pressure outlet at the far field of the relatively large room housing the display cabinet, so that ceiling, floor and walls were considered as no slip, V= 0 walls.
Figure 3 shows the pressure profiles in the room, in proximity of the air curtain, and the pressure out profiles reaching ceiling, floor and other far end walls.
[FIGURE 3 OMITTED]
For the 2 D mesh, the number of elements exceeded 31500 for the room and 12000 for the display cabinets and while testing for increasing the number of elements for another mesh trial to 61000 elements for the room and 22000 elements for the display cabinets, the error using second order upwinding of the vicinity of less than 9% was not justifying the excessive time of iterative computations.
Various values of the air velocity were assumed for the air curtains assuming other parameters constant, aiming at identifying the operating conditions yielding the lowest infiltration. A particular configuration was selected, based on specific set of geometrical parameters ([W.sub. DAG]= 0.04 m, Tilt Discharge angle ([alpha]) of 16 Deg., throw angle ([beta]) = 0 and H/[W.sub.DAG] ratio of 12) and Re of 3400, and tested for validation, revealing the validity of the simulation. In fact, when reproducing the experimental tests with a correct choice of the simplified model, an excellent agreement (about 6%) was found between the simulated and measured infiltration, H.K. Navaz et al. (20), at certain air velocities and as reported in. Though this agreement may be viewed as favorable, but there are uncertainty factors in both the numerical and the experimental outcomes.
Discharge Airflow Rate Variations
Figure 4 describes the velocity contours of different shapes at several values of the flow rate ranging from 0.02 to 0.13 Kg/s, allowing the calculation of the infiltration rate using equation (1).
[FIGURE 4 OMITTED]
The dimensionless C factor representing the infiltration rate, as seen in Figure 5, is decreasing upon the increase of the flow rate, Upon comparing the results of different geometrical values affecting the flow rates, i.e DAG size if changed from a width of 0.04064 m to 0.04171 m, it resulted in 2.6% error. Parameters used in carrying the simulations were for discharge tilt angle ([alpha]) = 0, Throw angle ([beta]) = 0, and aspect ratio H/W[.sub.DAG] = 12.
[FIGURE 5 OMITTED]
Tilt Discharge Positive Angle ([alpha]) Variations
Upon varying the tilt positive angle ([alpha]) shown in Figure 6, results of the variation of the infiltration rates are shown in Figure 6 for two different flow rates (0.05 & 0.08 Kg/s) with maximum values at angle [alpha] = 12.5 Deg., H/[W.sub.DAG] =16, and for both flow rates and minimum values at angle [alpha] > 16 deg.
[FIGURE 6 OMITTED]
Tilt Negative Angle ([alpha]) Variations
When changing the tilt angle to negative values, by extending the discharge grille to the direction of the room, the minimum values of infiltration rates are found as shown in Figure 7 for a flow rate of 0.04 Kg/s and H/[W.sub.DAG] = 16.
[FIGURE 7 OMITTED]
Vectors of velocity are shown in Figure 8 pertinent to the negative tilt angle variations of -10 and -2.5 degrees with more linear shape at ([alpha]) = -10, and upon closing all the back panel slots openings (leakage assumption of 5% only).
[FIGURE 8 OMITTED]
The minimum infiltration rate is found at tilt angle of -11[degrees] < ([alpha]) < -10.5[degrees] With infiltration rate C of 0.360 and for a flow rate of 0.05 Kg/s.
This infiltration rate at negative tilt angle is found to be less than the rate of the positive angle when taken about 10 degrees. (C= 0. 47019), resulting in preference for negative tilt angles.
The negative tilt air angle of 10[degrees] is so small, and for a certain vertical distance, will not face any obstruction from those in standing position in front of the display cabinet as shown in the velocity vectors of Figure 8.
Discharge Throw Angles ([beta]) variations
Upon varying the throw angle in the two directions, minimum infiltration rate is achieved at two values of ([beta]) = -3[degrees] & ([beta]) = 15[degrees] and at flow rate of 0.05 Kg/s. External perturbations and impingement of eddies of side flows explains the flexibility in the variation of the discharge angle without effecting the integrity of the air curtain. Figure 9 demonstrates the variation of the infiltration rate upon changing the discharge throw angle, when the discharge air angle ([alpha]) = 0.
[FIGURE 9 OMITTED]
Geometrical Variations H/[W.sub.DAG]
Two meshing systems were compared upon varying the ratio of the vertical distance between DAG and RAG and the width of DAG (H/[W.sub.DAG]). For a change of 3% of the ratio (H/[W.sub.DAG]) from 16 to 15.5, and a flow rate of 0.05 kg/s, and assuming linear proportional variation with respect to infiltration rate, it was found that errors over the calculation of infiltration rate C, becomes negligible. The same had been verified for flow rate of 0.13 kg/s. However for aspect ratio values of less than 12, it became difficult to obtain convergence of the solution.
The limitations over the decrease of the ratio H/W will enable the availability of feasible geometrical sizes of the display cabinet.
For values of H/[W.sub.DAG] of 12 and 16, infiltration rates are shown when varying discharge air angle ([alpha]).
Figure 10 illustrates the difficulty for curtain formation (velocity contour) for H/[W.sub.DAG]= 8.
[FIGURE 10 OMITTED]
Obstructions: Protruding Shelves and Cases
Allowing the upper shelf to protrude so that the extreme end of the shelf does not extend beyond the projection of the center of the discharge air grille, DAG, had allowed part of the discharged air flow to escape into the shelves void and creating smaller flow circulations. Figure 11 shows circulation inside the shelfs void when extending shelf and H/[W.sub.DAG] = 16 and discharge air angle ([alpha]) of 12 degrees.
[FIGURE 11 OMITTED]
Boxes and Cases of 0.16 and 0.20 m Near RAG
This study did not take into consideration the transient effects of hands penetrating the air curtain for short
Periods of time on the infiltration rates, nor the transit passage of insects on either sides. However, many applications of the refrigerated display cabinets, where inclined jets are utilized, filling of cases, or on the worst scenario, locating many boxes on the return grille (RAG) are witnessed which may hamper the integrity of the air curtain. Such stocking of goods (obstructions) is usually driven by the intent of maximizing the utilization of the limited volume of the display cabinet.
Figure 12 illustrates the increase in infiltration rate when locating a case with its height obstructing the air flow and making it more difficult for the formation of the air curtain.
[FIGURE 12 OMITTED]
The application of the CFD technique based on an experimental set up and as validated is proved to be a successful tool in identifying the geometrical and flow parameters of the inclined air curtain. It allowed the identification of the combinations of the various factors and the method of such combination to yield the optimum performance.
In trying to improve the efficiency of the inclined air curtain, flow rates should be increased but not excessively, so not to incur unwarranted energy costs and generate noise.
Tilt angle ([alpha]) plays an important role in determining the efficiency of the air curtain and the infiltration rates. Improved performance of the air curtain will be obtained upon implementing small values of positive tilt angle ([alpha]) < 10 degrees but more effectively, if negative angles in the vicinity of -10 degrees are employed.
Better performance of the air curtain can also be obtained, when the throw angle [beta] is in the range of -5 < [beta] < 5.
Similarly, a lower geometrical curtain ratio (H/W) can be provided, but if implemented, it will defeat the economic consideration of the inclined air curtain when utilized in a display cabinet, as smaller space for storing goods on shelf will be provided, resulting from lower H/W.
Upon Creation of internal turbulences within the shelves spaces, when extending the upper shelve to depth not to go beyond the projection of the centerline of the discharge air grille, DAG, improvement of the performance of the air curtain is anticipated.
Also, stacking boxes of goods on the lower shelf with their vertical height obstructing the flow of the air curtain, increases the infiltration rate. However, if the geometry of the curtain allows the negative tilt discharge angle, such goods can be stacked.
Finally, external perturbations resulting from pressure changes, whether derived from physical motions or other partial flows normal to the tilted jet plane, and on both sides of the tilted air curtain affects the optimum selection of such parameters. The CFD technique will be capable of identifying the implications of the change in the basket of these parameters.
This work could not have been completed without the support and help of many people and institutions namely Dr. Ali Hammoud of Beirut Arab University, Dr. Farid Khalil of Alexandria University, Dr. Homayan Navaz of Kettering University and Mr. Mazyar Amin of University of Washington who conveyed their enthusiasm and guidance in pursuing this work.
AT = eddy viscosity, kg*[m*.sup.1]*[s*.sup.1]
[A.sub.q] = eddy conductivity, W*[m*.sup.1]*[K*.sup.1]
b = width of jet or width of mixing zone, m
C = humidity ratio or moisture content, [kg.sub.water]/[kg.sub.dry air])
c = clearance volume factor
[C.sub.p] = specific heat of constant pressure, W*[kg*.sup.1]*[K*.sup.1])
[C.sub.v] = specific heat of constant volume ([W*[kg*.sup.1]*[K*.sup.1])
CFD = computational fluid dynamics
DAG = discharge air grill
h = enthalpy, kJ*[kg*.sup.1]
L = length of air curtain, m
m' = mass flow rate, kg*[s*.sup.1]
T = temperature, K
Tad = air dry-bulb temperature, K
[DELTA]T = temperature difference between case inside and air curtain inlet, K
P = pressure, Pa
RAG = return air grill
U = momentary velocity in x direction, m*[s*.sup.1]
V = momentary velocity in y direction, m*[s*.sup.1]
x = rectangular coordinate in x direction (along the length of the air curtain), m
y = rectangular coordinate in y direction, m
Pr = Prandtl Number
Re = Reynolds Number, based on DAG width
[rho] = air density (kg*[m*.sup.1]
[mu] = dynamic viscosity (kg*[m*.sup.1]*[s*.sup.1]
0 = air curtain inlet
amb = ambient
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|Author:||Traboulsi, Samir R.; Hammoud, Ali; Khalil, M. Farid|
|Date:||Jul 1, 2009|
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