5. mech - ijmperd - -numerical predictions of air distribution - ammar m. hadi

www.tjprc.org [email protected]

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN(P): 2249-6890; ISSN(E): 2249-8001 Vol. 4, Issue 3, Jun 2014, 35-52 © TJPRC Pvt. Ltd.

NUMERICAL PREDICTIONS OF AIR DISTRIBUTION IN AIR CO NDITIONED SPACE

ALA’A ABBAS MAHDI & AMMAR M. HADI

Department of Mechanical Engineering, Faculty of Engineering, University of Kufa, Kufa, Iraq

ABSTRACT

Physical

The three-dimensional numerical study of turbulent recirculating for air distribution in space. The study solved the

partial differential equations by using finite-volume method. By using Ansys-FLUENT 6.3.26 to simulate the complex

flow inside the physical model. Carried out the process of verifying the accuracy of the results obtained from the program

and compare them together. The results of numerical model were compared with experimental predications of previous

researchers. These comparisons show a good agreement. Therefore, the simulation of non-isothermal turbulent flow within

the room, was made using three principle geometrical arrangement of the room with different locations of supply opening,

which built by gambit(2.2.30) program. The predicted flow were plotted and discussed for buoyant flow. The study

demonstrates that the flow behavior depends on location of the opening supply (up and down) and on the location of the

obstruction. These parameters was modeled separately to understand how each of this parameters affects the flow pattern.

The “Air Diffusion Performance Index” effected by these parameters greatly, and, found that the location of the opening

supply is related directly to load centered. Also, the present work results show that the Coanda effect has large effect on the

general form of air distribution, and then, on thermal comfort.

KEYWORDS: Numerical Simulation, Cold Air Distribution, Temperature Profile, Velocity Profile, Coanda Effect

INTRODUCTION

People occupies indoor almost 90% of their time, so it should be available the requirements of comfort and purity

of the air inside the enclosed spaces as comfortable as possible, [1]. The building ventilation his several purposes to

remove or supply heat to maintain a acceptable thermal distribution. The value of velocity and air temperature and

humidity are important in human comfort in occupied zone, so the extreme values of cooling or heating may be

Undesirable to the occupants of the zone. That Prediction the distribution of air temperature and facilitates the task of

conducting accurate designs for air diffusers systems in place.

Distribution of air inside the indoor spaces were attention researchers as Fang et. al. (1988) [3], studied the

distribution of air using finite difference method and establish a specific a computer program that to show the temperature

distribution inside the space and calculation (ADPI). a sidewall grill are carried out six air flow rates supply compared with

the corresponding published experimental values.

Gamboa (2001) [4], studied numerically the influence of temperature differential (T.D.) between the inlet supply

and the space of occupied zone on throw and drop, it obtained that decrease in this differential of temperature (T.D.)is good

to achieve ceiling effect (Coanda effect) to be larger and vise versa, also to be observed this effect on throw and drop.

Some rough guide lines are appear to select the supply unit type dependent on temperature differential (T.D.).

Srebricet. Al. (2002) [5] concluded that the momentum method ideal for the displacement diffuser.

36 Ala’a Abbas Mahdi & Ammar M. Hadi

Impact Factor (JCC): 5.3403 Index Copernicus Value (ICV): 3.0

The box method were that good method for the valve, slot and nozzle supply, combine in front of them should use, since

the momentum method was not recommended for above types.

Essam (2006) [6], studied the balance between human comfort and air quality in places of health care to optimize

air quality. It was found that the selection air distribution system plays an important role for achieving the optimum air

quality beside the optimum comfort level. The numerical tool was found to be so effective to predict air flow pattern in the

healthcare facilities at reasonable costs and acceptable accuracy. Good architectural design allows the HVAC system

designers to properly locate the supply outlet and extract ports in the optimum locations.

Cai et. al. (2010) were compared a analytical and numerical model to air distribution. The results for different

conditions obtained for the velocity and temperature distribution in a room. The results shows that the air circulation is

generated and the air eddies at the corner. That occurs at both the ceiling and wall air supply.

Son et. al. (2011) studied compares between two air distribution systems. The supply air with humidity and

contaminant were modeled for an underfloor system and an ceiling air distribution system. Three different locations of

supplied diffuser were suggested.. For overhead air distribution, the inlet is located on the ceiling with slower and cooler

inflow. Three inlet angles are considered. For both systems, the air return location is on the ceiling at the same place.

The velocity, temperature, relative humidity, and contaminant concentration distributions in various cases for both systems

are analyzed Results were presented details about the movement of air in enclosed spaces in terms of human comfort and

air quality that are useful for office building. It is found that underfloor system shown a good performance than ceiling

system in contaminant removal while maintaining the same thermal comfort condition.

THEORETICAL FORMULATION

The mathematical formulation of convection problems follows the basic conservation principles that govern

general fluid motion namely the conservation of mass, momentum, energy equations at constant density in a Cartesian

coordinate as well as the transport equation for turbulent velocity can be presented as follows [9].

(1)

X – Direction (U Momentum)

(2)

Y – Direction (Y momentum)

(3)

Z – Direction (W Momentum)

(4)

And energy conservation equation

Numerical Predictions of Air Distribution in Air Co nditioned Space 37


(5)

The modeled transport equations for k and ε in the realizable (k, ε) model are, [9]:

k - Equation

(6)

ε - Equation

(7)

The recommended values of the empirical constant and functions are given in Table (1). These values represent

what is considered the standard (k-ε) model, [9].

Table 1: Constants for the "Standard" (k-ε) Model

Cµ C1 C2 σk σε

0.09 1.44 1.92 1.0 1.3 BOUNDARY CONDITIONS

The mechanically ventilated problem considered in present study requires the solution of the complete

Navier-Stock equations, which are elliptic type. It implies that the condition at any point in the flow can be influenced by

other points. Therefore, it is necessary to supply boundary conditions for variables at all the boundaries of the flow domain.

The typical flow domain in the present work is a three-dimensional rectangular room with different locations of inlet

opening with change the location of obstruction. The solution domain is bounded by walls, floor, ceiling and the boundary

of the heat obstruction.

The general boundary conditions specified for the present study are as follows:

Boundary Condition at Inlet

• Velocity component (U): A uniform profile is prescribed for U-velocity at inlet (U=Uin).

• Velocity component (V): Zero value is given to the V-velocity in the inlet (V=0).

• Velocity component (W): Zero value is given to the W-velocity in the inlet (W=0).

• Temperature (T): A specified value is given to the temperature at inlet (T=Tin).

Boundary Condition at Outlet

The outlet velocity is computed from mass balance on the room as given by the following:

Uout=Uin (Ain/Aout)

The vertical velocity is considered zero (V=0, W=0)



The Obstruction Heat and Earth Heater Boundary

The heat obstruction surfaces were treated as a solid. This means that the following variables (U,V, and W) are

treated as previous section. On the other hand, a specified value is given to the heat flux at the heat obstruction and heat of

the fine earth strep surfaces.

Boundary Condition at Solid Boundaries

• Velocity component (U, V, and W): In the present study the solid surfaces are stationary so the velocity

components (U,V, and W) are set to zero.

• Temperature (T): The solid surfaces temperature are adiabatic.

• Turbulence kinetic energy (K): the gradient of the turbulent kinetic at solid surfaces is set to zero, (i.e.( )j

wall=0, as( )y wall=0).

• Dissipation rate (ε): The value of the dissipation rate at solid surfaces is zero ((ε)wall=0).

CASES OF TEST STUDY

The test physical model numerically [3] were dimensions as (6.10 m wide x 3.66 m long x 2.74m high) simulating

an interior room of a multi-story office building. The power input to room consisted of uniform heating loads from finstrip

heaters located around the center of the room floor and having a total heat output of (88.3 W/m²) over a (3.66 x 1.52 m)

floor area, and a concentrated load composed of a (0.97 x 0.91 x 0.3 1 m) angle iron framework installed (0.20 m) from the

wall which opposite to opening inlet wall, and having a heat output rate of (327.9 W/m²). A grille testing

(0.61 m W x 0.15 m H) was located in the middle of a (3.66 m L), with its horizontal high at (0.15 m) from the ceiling.

A (0.76 m W x 0.42 m H) return grille was located under the supply grille, (0.71 m) from a floor.

Mathematical modeling was performed to simulate four tests which are tabulated with their temperatures

respectively in Table (2). All walls were assumed as adiabatic. A 50% free area air diffuser used from the grille.

The physical model shown in Figure (1)

Grid of Models

The resolution of the grid is a strong factor in the magnitude of the overall simulation error. Clearly as the cell

dimensions are reduced, the error is reduced. Time and computational constraints, however, limit the resolution of the

computational mesh. A grid of non-uniform intervals is employed in a room. A grid size is (∆x = 58mm) in x-direction,

(∆y = 54mm) in y-direction, and (∆z = 40mm)in z-direction are employed as shown in Figure (2), and this size of mesh is

twice that uses in published paper [3] and it is same size for thesis [10], this size of mesh give a reasonable agreement with

experimental data.

Bartak [11] obtained that both the fine and coarse grid calculation give very close the results were very close

results. And both fine and coarse grid gat data are slightly higher than the measured, and Mora [12] deduce that ”In both

cases, the test room with domain grids ranging from case one (8x8) to case two (73x57) cells, the main recirculating flow

predictions are in agreement with experimental airflow visualizations”.



Computational Details

The gambit (2.2.30) program was used to draw the geometry for room then export it to fluent (6.3.26) program.

The fluent (6.3.26) was used to solve the governing equations for elliptic (recirculation) flows through a three-dimensional

mechanically ventilated room with heated floor and obstruction have been solved numericallybased on finite volume

method by an iterative method in the present work. The general three-dimensional formulation of these equations are

described in previous section. The dependent variable in the case of the problems considered are three component of

velocity (u, v, and w), pressure (p), temperature (T), turbulence kinetic energy (k), and it’s dissipation rate

(ε). The SIMPLE algorithm was adopted in solving these governing equations.

The ADPI calculations were based on predicted air temperatures and velocities at (960) locations, which were

uniformly distributed throughout the occupied zone. The momentum method [5] is used formodelingthe inlet opening

(grill), this method is one of methods to simulate the openings inlet supply.

AIR DIFFUSION PERFORMANCE INDEX (ADPI)

Indoor air movement is very important in evaluating the ventilation design and determining the thermal comfort in

a building. Complaints due to 'draft' or 'unwanted local cooling of the human body caused by air movement' would be

reported in poorly ventilated spaces. Therefore, values of the air speed are also specified in the common design criteria and

appear in thermal comfort indices. Air speed is used to determine the effective draft temperature (EDT), from which the air

diffusion (distribution) performance index (ADPI) can be calculated. This parameter is useful in describing the diffusion

performance of air for a diffuser in a ventilated space, [13].

The effective draft temperature (EDT) was defined as, [3&13]:

EDT = (Tx-Tr)-8(Vx-0.15) (8)

Where, (Tx) is the local air stream dry-bulb temperature in °C, (Tr) is the mean room dry-bulb temperature in °C,

(Vx) is the local air stream velocity in m/s.

The air diffusion (distribution) performance index (ADPI) is a percentage that is defined by the number of points

measured in an occupied zone where EDT is within the set limit (>-1.7°C and <1.1°C) over the total number of points

measured in it.

COANDA EFFECT

When a primary airstream discharged from a supply outlet flow along a surface, the velocity of the primary

airstream is significantly higher than that of the ambient air, and a lower pressure region is formed near the surface along

the airflow, as shown in Figure (3). Consequently, induced ambient air at a comparatively higher pressure presses the air

jet against the surface, even when it is a curved surface. Surface a phenomenon is called the surface effect or

Coanda (or Conda) effect, [1].

Friction between the air jet and the boundary decreases the centerline velocity of confined air jets. However,

because of the surface effect, the throw of a confined air jet is longer [1], and this effect countering any downward

buoyancy forces and delaying the drop into the occupied zone as shown in Figure (4), [14].



VALIDATION

The results for the present study (for a room) were compared with experimental and theoretical data of Fang [3]

and tabulated in Table (2), the comparison depend on Air Diffusion Performance Index (ADPI). These results include flow

patterns and their comparisons showing in Figure (5) to (8).

The comparison obtained a good agreement between the present work and published data and graphic,

“The difference between experimental and numerical value is between 10% and 20%, considering a number of similar

results reported in the field of indoor airflow measurements and simulations”[11]. The comparison with Fang data

graphic[3] were done to verify the result of the present program in order to use this program to predict a more general cases

and other geometries that are introduced in previous section.

RESULTS AND DISCUSSIONS

One of the most important aims for fluid circulation in a space with air is to promote and direct air movement in

space, being one of the environmental conditions for the occupant of room. In order to do the object of heated earth and

obstruction within an grill as opening supply, this opening supply must have a proper location to maintain an acceptable air

motion and temperature in the working of occupant zone.

There are many factors that affect the flow characteristic and temperature distribution insidethe occupation zone

of a ventilated zone as locations of the openings and obstruction, and increase the load by add a window or any heat

source. These factors are discussed below.

According to fourth situation listed Table(2) the inlet flow rate and temperature are taken to be

(54.86 m³/h-m², 292.8 K).Due to exist the loads and openings in middle of the width of occupied zone, so all figures below

are taken at section in a half z-axis of the room as it look in Figure (9). The distance between the opening supply(high line

of the opening supply) and ceiling is always to contrast with respect to height of opening supply itself (h), as (0.5h) or (2h).

Table 2: Air Diffusion Performance Index (ADPI) Comparison for the Cases of the Present Work with Published Data

No. Inlet Flow

Rate (m³/h-m²) Velocity

Inlet (m/s) Temperature

Deference

ADPI Max Error

(± %) Experimental [3] Theoretical [3] Present Work

1 10.97 1.487 17.20 68 64 64 6.25 2 18.29 2.48 10.36 79 80 76 3.94 3 36.58 4.96 5.18 82 81 80 2.5 4 54.86 7.436 3.452 74 73 75 1.33

Temperature deference = Troom average – Tsupply

Case (I)

The influence of the opening supply location presents results for the following, Figure (10):

• (1.5h) from ceiling





• (0.0h) from ceiling (i.e. adhered with ceiling)

Where (h) is height of opening supply.

The air temperature in occupied zone in the first two locations (a,b), increase and this causes decrease

ADPI (air diffusion performance index), while in the second two locations (c,d), an opposite results are shown, i.e. the

temperature for the occupied zone is decreased and ADPI is increased, and this results favorite for thermal comfort

Figures (11), the results for this case are given in Table (3).

According to ASHRAE [15], for height of the opening supply, the present results obtained good identical.

The reason for increase the occupied zone temperature and decrease ADPI with increase the distance between the opening

supply and ceiling conditions (a, b) is due to occurrence the eddy near outlet opening, and this mean that the short circuit

happening between the inlet and outlet (i.e. the low temperature air leaving before benefiting from it at whole form) and in

this conditions don’t benefit from Coanda effect (which adhered the air with ceiling), as shown in Figures (12).

On the other hand, by benefit from Coanda effect arrival the air to end room for conditions(c, d), this very distinct

through contours Figure (13), which obtained arriving the air to opposite side (identical to [1]) with large difference from

other cases where decreasing of the air velocity which arrive to the opposite wall with decrease the distance between the

inlet opening and ceiling, then advantage from inlet cold air in larger form to room, and this shown by comparison in

Figure.(14) which show that condition(d) has EDT (effect draft temperature) larger than the others firstly (to three quarter

of the occupied zone) then the other conditions begin to rise in large form and noticeable until they pass the required

degree for EDT (1.1) of which has negative effect on overall average for ADPI.

The other reason for rises ADPI is the terminal velocity lifting (increasing) which going to rise the velocity in

occupied zone specially (identically to [1]) and in all room generally, in agree boundary for velocity according to

[14] which recommended that the velocity must to be less (0.25 m/s). All the above occurs without exist obstruction in

ceiling (i.e. flat) and this preferred by carrier [16], with high side wall grill.

Table 3: ADPI and Average Temperature for Case (I)

Conditions The Distance between

Opening Supply and Ceiling ADPI (%)

Average Temperature for Occupied Zone (K)

B 2.0 h 67.0 296.24 A 1.5 h 71.2 296.21 * 1.0 h 75.0 296.13 C 0.5 h 78.3 296.08 D 0.0 h 84.3 296.94

* Comparison level.

Case (II)

The results obtained for these case of different locations for the obstruction toward the wall which contains the

opening air supply and return air opening, every step approximate (1.4m), in every step change the location of the opening

supply to get the preferable.



• Conditions (a, b, and c)

In these conditions move the obstruction (1.4m), and change the location of the opening supply up in two steps

every one (0.5h), Figure (15).

o (1.0h) from the ceiling

o (0.5h) from the ceiling

o (0.0h) from the ceiling (i.e. adhered with ceiling)

The results in Table (4) obtained that condition(c) is more suitable according to ADPI value, from Figure (16) it is

obtained a comparison among them by line along centered the occupied zone, i.e. (i, j, k,) are (0.28,1.02,1.83m) to

(5.31,1.02,1.83 m). The reason to up ADPI with decrease the distance between the opening supply and ceiling can notice

by showing Figure (17), where obtained decreasing in room temperature with lifting the opening supply to ceiling.

The contour line number(3) of the temperature distribution in Figure (17a) go down then back up because the

emanating heat from the obstruction in addition to small air eddy whichformed behind the obstruction as shown in

Figure (18a), this eddy will prevent this region to benefit from the air supply in direct and large form, but with lifting the

opening supply to ceiling can notice disappearance this small eddy, Figure (18b) & (18c), then allowing the contour line(3)

in Figures.(17b) & (17c) to go down more and more in occupied zone (up and behind the obstruction). Addition to this

reasons were mentioned in case (I).

Table 4: ADPI and Average Temperature for Case (II), Conditions (a, b, & c)



Average Temperature for Occupied Zone (K)

A 1.0 h 74.0 295.92 B 0.5 h 79.6 295.85 C 0.0 h 83.5 295.78

• Conditions (d, e, and f)

The obstruction moves twice increment toward left wall, the step in this time is (1.45m), as shown in Figure (19).

Through ADPI in Table (5) showed that condition (e) is better off than conditions (d and f). As shown in Figure (20), for a

line along occupied zone, can see the line for condition (e) is the preferable. Figures.(21) show the contours lines of

temperature distribution, notice that contour (3) in Figures (21a) & (21b) to begin lower than in Figure (21c), this means

that drop in room temperature in conditions(d and e) are more than condition(f).

When comparison between Figure (21a) with Figure (21b) cannot notice large drop in temperature but the reason

to rise ADPI between condition (d) and condition (e) is the velocity distribution, and this shown through Figures (22a) &

(22b) where can see that the location of eddy is crawl slightly to room center, and this mean increase the air velocity in

middle of the room for condition (e).

Table 5: ADPI and Average Temperature for Case (II), Conditions (d, e, & f)



Average Temperature for Occupied Zone(K)

D 1.0 h 85.7 295.52 E 0.5 h 87.0 295.48 F 0.0 h 84.9 295.47



CONCLUSIONS

The importance of computational modeling for indoor flows was demonstrated. To simulate internal flow properly

all factors have to be clearly detailed. The opening supply location has a large effect on the flow pattern, and the effect of

this location is changing with moving the obstruction, These parameter was modeled separately, trying to understand how

each parameter affects the flow pattern. The following observations were Conclude:

The better location of the opening supply is correlated with heating load centering. It was found that, the height of

the opening supply (in y-axis) is direct proportion with centered of the load (in x-axis), with this relation the

non- isothermal flow (cold air) can absorb main load from the occupied zone, therefore the climate of the occupied zone is

fine in accordance with thermal comfort condition. This happen in mixing ventilation type when supply and outlet

openings in same side. Benefiting from Coanda effect is very important, particularly in long room (longer than popular

length). Coanda effect isvery useful to arrive the cold air (which heavy comparatively) to farther point possible. So the

terminal air will be in range of thermal comfort and don’t occurrence the draft.

SUGGESTIONS FOR FUTURE WORK

In this section some proposals are made for improving and extending the present numerical model.

These are listed below:

Possibility of studying the effect of other factors such as size of opening supply, size and number of window and

heat transfer between flow and walls. The geometry of room in the present study gives a good agreement for cooling case

(in spring season), but is it success in winter season with hot flow supply?, and the ability to relate with Iraqi climate.

Potentiality experimental studying using recent devices and sensors to measure the main parameters as

temperature and flow velocity

Figure 1: General Structure for a Room Figure 2: Mesh Distribution for Three Dimensional Domain for a Room

Figure 3: Formation Coanda Effect by Figure 4: Formation Coanda Effect by Opening Supply in the Ceiling, Ref [13] Opening Supply at High Side Wall, Ref [14]



(a) (b)

(c)

Figure (5): Distribution of Calculated Velocity Vector in Center Plane in a Room Inflow Rate (10.97m³/h-m²), (a) Experimental Visualization [3], (b) Theoretical by Fang [3], (c) Present Work

(a) (b)

(c)

Figure (6): Distribution of Calculated Velocity Vector in Center Plane in a Room for Inflow Rate (18.29m³/h-m²), (a) Experimental Visualization [3], (b) Theoretical by Fang [3], (c) Present Work



(a) (b)

(c)

Figure (7): Distribution of Calculated Velocity Vector in Center Plane in a Room for Inflow Rate (36.58m³/h-m²), (a) Experimental Visualization [3], (b) Theoretical by Fang [3], (c) Present Work

Figure 8: Distribution of Calculated Velocity Vector in Center Plane in a Room for Inflow Rate (54.86m³/h-m²), (a) Experimental Visualization [3], (b) Theoretical by Fang [3], (c) Present Work



Figure 9: Studied Planes

Figure 10: The Opening Supply Locations, Case (I), (1.5h)

(a) - (1.5h) (b) - (2.0h)

(c) - (0.5h) (d) - (0.0h)



(e) - (1.0h)

Figure 11: Distribution of Calculated Air Temperature Contours, Case (I), a-(1.5h), b-(2.0h), c-(0.5h), d-(0.0h), e-(1.0h)

(a) - (1.5h) (b) - (2.0h)

(c) - (0.5h) (d) - (0.0h)

(e) - (1.0h)\

Figure 12: Distribution of Calculated Velocity Vector (Fixed Vector Length), Case (I) a- (1.5h), b- (2.0h), c-(0.5h), d- (0.0h), e-(1.0h)



(a) - (1.5h) (b) - (2.0h)

(c) - (0.5h) (d) - (0.0h)

(e) - (1.0h)

Figure 13: Contours of Velocity Air Distribution, Case (I), a- (1.5h), b-(2.0h), c- (0.5h), d- (0.0h), e- (1.0h)

Figure 14: Effect Draft Temperature (EDT) Figure 15: The Opening Supply Locations for First for Different Opening Supply Locations, Case(I) Obstruction Location, Case(II), Conditions (a), (1.0h)



Figure 16: Effect Draft Temperature for Different Opening Supply Locations, Case (II), Conditions (a, b, &c)

(a) - (1.0h) (b) - (0.5h)

(c) - (0.0h)

Figure 17: Calculated Air Temperature Distribution Contours, Case (II), Conditions (a, b, &c), a-(1.0h), b-(0.5h), c-(0.0h)

(a) - (1.0h) (b) - (0.5h)



(c) - (0.0h)

Figure 18: Distribution of Calculated Velocity Vector (Fixed Vector Length), Case (II), Conditions (a, b, &c), a-(1.0h), b-(0.5h), c-(0.0h)

Figure 19: The Opening Supply Locations for Second Obstruction Location, Case (II), Conditions (d)-(1.0h)

Figure 20: Effect Draft Temperature for Different Opening Supply Locations, Case (II), Conditions (d, e, f)

(a) - (1.0h) (b) - (0.5h)



(c) - (0.0h)

Figure 21: Distribution of Calculated Air Temperature Contours, Case (II), Conditions (d, e, & f), a-(1.0h), b-(0.5h), c-(0.0h)

(a) -(1.0h) (b) -(0.5h)

(c) -(0.0h)

Figure 22: Distribution of Calculated Velocity Vector (Fixed Vector Length), Case(II), Conditions (d,e,&f), a-(1.0h), b-(0.5h), c-(0.0h).

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5. mech - ijmperd - -numerical predictions of air distribution - ammar m. hadi

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