three-dimensional numerical study on flow and thermal ...m) to investigate the indoor air...

4th International Conference On Building Energy, Environment

Three-dimensional Numerical Study on Flow and Thermal Characteristics of Wall Jet Diffuser in an Enclosure

K.P. Gokulraj *, S. Tiwari and M.P. MaiyaDepartment of Mechanical Engineering

Indian Institute of Technology Madras, Chennai 600036, India Email: *[email protected]

SUMMARY The thermal comfort of an air-conditioning system also depends on the airflow pattern inside an enclosure. The effective thermal comfort of the indoor space cannot be achieved by simply increasing the air conditioning capacity nor by the number of supply inlets. Adequate cooling requires minimization of the temperature of air in the mixing zone followed by removal of mixed air through the return inlet. Objective of the present study is to investigate the effect the configuration of wall jet diffuser on thermal comfort in an enclosure. Effect of changes in cooling load and supply outlet angle of the diffuser has been studied on thermal comfort performance of the cold air jet. Flow is considered to be three-dimensional, transient, turbulent and incompressible with Boussinesq's approximations assumed to be valid. Computations are carried out using commercial software ANSYS Fluent 16.1 and the results are validated against those reported in literature. For the enclosure, flow rate is varied by keeping the room average temperature constant and thermal comfort is analysed in terms of effective draft temperature and air speed. Special distinctions are used to show the hot and cold zones for the analysis of thermal comfort. Results indicate that increase in the outlet angle and decrease in the cooling load satisfies the thermal comfort.

INTRODUCTION Thermal comfort has gained more emphasis due to people spending most of their time in indoor space. Therefore, people expect the indoor environment to be as comfortable as possible. According to American Society of Heating, Refrigeration and Air conditioning Engineers (ASHRAE Handbook, 2009), thermal comfort is defined as the condition of mind that expresses satisfaction with the thermal environment. Discomfort is expressed as a result of drafts and undesirable local cooling of human body due to low temperature. In order to avoid discomfort and to meet the thermal requirements of the occupied space, it is necessary to ensure proper air distribution. Primary factors affecting the comfort of the occupants are air temperature, air velocity, turbulence intensity, relative humidity and noise level of diffuser. Complaints received from occupants in a survey conducted by the International Facility Management Association pertains to the degree of hotness and coldness. The occupants were not able to distinguish between a draft, degree of hotness and coldness and stuffiness. They often complained about the room being stuffy which occurs mainly due to lack of ventilation, varying solar load, occupancy load and changes in space envelope.

There have been several researches conducted using Computational Fluid Dynamics (CFD) and full-scale models to study the effect of indoor air distribution on thermal comfort and indoor air quality. Zhang et al. (1992) conducted

an experiment in a full scale test room (5.5 m7.3 m2.4m) to investigate the indoor air distribution in isothermal andnon-isothermal conditions. They reported that turbulence inthe indoor air distribution is mainly generated in the diffuserjet region and is distributed to other parts of the room at lowturbulent fluctuation of air speed. Thus the mixing of primaryand secondary air would take place above the occupied zoneto avoid discomfort. They determined that indoor airdistribution is mainly affected by the internal heat load. Chowand Wong (1994) conducted an experiment in a full scaletest room (4.1 m2.1 m2.6 m) to investigate the effect ofArchimedes number (Ar), Reynolds number (Re) and Jetnumber (J) on thermal comfort in non-isothermal conditions.They reported that Re and J increase linearly while Ardecreases linearly with increase in flow rate. However, thereexists no correlation between the Air Diffusion PerformanceIndex (ADPI) and these numbers. Miller (1974) performed anASHRAE research project in which he introduced theconcept of ADPI and estimated its values for cooling loadsbetween 65 W/m2 – 235 W/m2 for different flow rates and fivetypes of diffusers. According to Miller and Nash (1974) thecritical factor for determining the ADPI in cooling mode for agiven enclosure is determined by the ratio of isothermal jetthrow (T) of the diffuser to the characteristic length of theroom (L). Chung and Lee (1996) performed three-dimensional numerical study on effect of convective solarheat gain from windows for different locations of supply outletand return inlet. The thermal comfort is quantified andestimated with the help of two indices, viz. ADPI andPercentage of people dissatisfied (PPD) due to draughtsensation (DR). They found that the thermal comfort isaffected at higher supply air velocity and lower airtemperature. They also found that the locations and numberof supply outlet and return inlet play an important role in thebehaviour of indoor air distribution. Earlier diffuser selectioncriteria based on thermal comfort were proposed only for fivediffuser types with cooling load in the range of 65 W/m2 to250 W/m2, which are higher than the updated cooling loadvalues. Due to the concerns associated with energyefficiency of the buildings, reduction in internal cooling loadof buildings by adoption of various measures, such as highinsulation material and energy efficient lighting systems,were obtained. Accordingly, the cooling load contributed bythe lighting system and the floor is estimated to be 25 – 50W/m2. Liu et al. (2017) conducted experimental studies toupdate the guidelines for diffuser selection using ADPIconcept for 15 types of overhead diffusers at low coolingloads in the range between 25 – 50 W/m2. They can be usedas minimum set-points for the Variable Air Volume (VAV)system. According to ASHRAE Standards the acceptable T/Lratio is in between the range 0.7-2.1 for high side wall grillsat cooling loads less than 33 W/m2 .They estimated T/L ratioto be in between 1.2-2.2 at 25 W/m2. Similarly, the T/L ratioin ASHRAE standard is reported to fall between 1-1.9 at 65W/m2 while Liu et al. (2017) estimated T/L ratio to fall in the

ISBN: 978-0-646-98213-7 COBEE2018-Paper268 page 797


range 1.7-2.2 at 50 W/m2. They found that room height, floor area and number of diffusers have strong influence on the diffuser performance.

In order to improve the diffuser performance on thermal comfort it is necessary to understand the indoor air distribution. If the diffuser is designed in such a way that the jet is not high enough to create the necessary Coanda effect to overcome the negative buoyancy effect, the jet falls into the occupied zone. This creates excessive drafts and leads to formation of stagnation regions in the occupied zone. Poor indoor air distribution can affect both the thermal comfort as well as the indoor air quality. Thus the objective of present study is to numerically investigate the effect of supply outlet angle and cooling load on thermal comfort using the indicies of ADPI and DR.

ASSUMPTIONS Flow is considered to be three-dimensional,

transient, turbulent and incompressible withBoussinesq approximation being valid.

Only internal cooling load is assumed to be presentand external cooling loads due to infiltration,transmission and fenestration are neglected.

No pollutants have been considered to be present.

PROBLEM STATEMENT A three-dimensional rectangular room of length (L) 6 m, width (W) 3 m, and height (H) of 3 m has been considered. The schematic locations of the supply outlet and return inlet are as shown in Fig. 1.

(a)

(b) Figure 1. (a) Schematic of the Computational domain (b) Schematic of the longitudinal vertical mid plane

The dimensions of the supply outlet and return inlet are fixed. Their width (w) and height (h) are 0.4 m and 0.03 m respectively. The temperature profile at the supply outlet is assumed to be uniform. The supply outlet and return inlet are fixed at 0.3 m below the ceiling and above the floor respectively as shown in the Fig. 1b. The Supply outlet angle ( ) is varied from 450, 0o with reference to the horizontal dotted line as shown in Fig. 1b. The Reynolds number is calculated based on the hydraulic diameter of the inlet.

Table 1. Simulated cases for different heat loads

Cooling load ( q )(W/m2)

Supply air

temperature (

oT ) ( C )

Supply air

velocity (Vo) (m/s)

Room average tempera

ture (Tavg)

( C )

Re

50 (100 %) 16 4.73 24 18023 37.5 (75 %) 16 3.545 24 13455 25 (50 %) 16 3.021 24 11466

Computations are carried out by fixing the room average temperature as constant for two different supply outlet angles ( ) and cooling load of the enclosure as shown in the table1. For each cooling load the supply outlet angle is varied fortwo different = 45o, 0o. The wall temperature (Tw) of theenclosure, except the floor is maintained at 24 C . Thecooling load is applied at the floor.

GOVERNING EQUATIONS AND BOUNDARY CONDITIONS Governing equations

The mass, momentum and energy equations are represented in Cartesian tensor form as, Mass conversation:

(0i

i

u

x

(1)

Momentum conservation:

()

i j ii j i avg

j i j j

u u pu u g T T

x x x x

(2)

Energy conservation:

( )p ip i

j i i

C u T Tk C u T

x x x

(3)

where, is the density, ui, uj, uk are the velocity components along x, y, z – Cartesian coordinate direction. P denotes the pressure, denotes the dynamic viscosity. In the momentum equation, the last term denotes the buoyancy force in which gi indicates gravitational acceleration in the ith direction. Tavg is the reference temperature (room average temperature). In the energy equation Cp, T and K represents the specific heat capacity, temperature and thermal conductivity of the fluid respectively. For details about the Reynolds stress ( ' 'i ju u ) and the turbulent heat flux andstandard k- the reader may refer to Launder and Spalding (1974) .

BOUNDARY CONDITIONS Uniform temperature distributions are assumed at the inlet. The boundary conditions for supply outlet, return inlet, walls, ceiling, and floor in Figure 1 are:

Inlet:0 0( 45 ) , , 0

o u V Sin v V Sin w ,

0( 0 ) , 0o u V v w ,

0T T , 2 21.5 ok I V ,

0.75 1.5C k

l

Outlet: Pressure outlet ( p p )



Ceiling1, short wall2, long wall3: No-slip andIsothermal boundaries ( 0u v w ,

wT T , 0k ,

0 )

Floor: Constant heat flux (

T q

y)

GRID INDEPENDENCE STUDY The commercial software ANSYS ICEM 16.1 is used for generation of a non-uniform structured mesh. A very fine mesh is created near to the supply outlet region, jet region and walls and a coarser mesh is created in the occupied zone. Grid 1 (G1), Grid 2 (G2) and Grid (G3) contain 7.5 51010 510 and 15 510 cells respectively.

(a)

(b) Figure 2.Comparison of grid independence study (a) Jet zone axial velocity (b) Schematic of grid mesh for the computational domain

As observed from Fig. 2, there is no significant difference between results of grids G2 and G3 . So, Grid 2 is selected for all the computations. The mesh sensitivity analysis is performed for = 0o and q = 37.5 W/m2 as shown in Fig. 2. Due to symmetry of the computational domain only half of the computational domain is used for the simulation.

NUMERICAL TECHNIQUE The pressure velocity coupling used in the finite volume method based commercial software Fluent 16.1 is solved by Semi Implicit Method for Pressure-Linked Equation (SIMPLE) method. The spatial discretization is performed for

the governing equations by the least square cell-based approach to compute the solution variables at cell centres and second order method is used to compute the pressure values at the cell faces. Convective terms are discretised by second order upwind and diffusive terms by central difference scheme. The convergence criteria is 10-5 for all the equations.

PERFORMANCE PARAMETERS The mathematical model for DR was developed by Fanger (1970) to evaluate the significant influence of air turbulence on the sensation of draft in the occupied zone. The value of DR is estimated by the following formula

0.6234 ( 0.05) (0.37 3.14) /100PD T V VI (4)

where, I, T, V is the turbulent intensity, local air temperature, local air speed respectively. The value of V is taken as 0.05 m/s if the estimated value of local air speed is less than 0.05 m/s. The DR value is taken as 100% if estimated DR is greater than 100%. . The ADPI mathematical model is developed by Nevins and Miller (1974). ADPI is used to evaluate the diffuser performance for the cooling conditions. ADPI is the percentage of points in the occupied zone, where the air speed is less than 0.35 m/s and EDT is in between the range -1.7 oC and 1.1 oC. According to ASHRAE Standard, ADPIis satisfied if, 80% of the points in the occupied zone satisfiesthe thermal comfort criteria mentioned for the EDT and airspeed.

100oN

ADPIN

(5)

where No is the number of points in the occupied zone which satisfies the thermal comfort criteria and N is the total number of points in the occupied zone. The EDT is measured by the following formula

EDT ( ) 8( 0.15)avgT T V (6)

where, T, Tavg and V are the local air temperature in oC, room average temperature in oC, and local air speed in m/s in the occupied zone respectively. The EDT is defined by Koestel and Tuve, (1955) as the temperature difference at any point in the occupied zone and the control zone. To satisfy the thermal comfort criteria the EDT must be in the range between -1.7 oC and 1.1 oC. The value lesser than the former and greater than the latter represent the cold zone and hot zone respectively. The separations of EDT zones are as defined by the Houghten et al. (1938)

RESULTS AND DISCUSSION Validation of computations Only a few experimental works have been reported in literature to study the performance of diffusers. However, the computational accuracy has been confirmed by validating the results with those reported in the literature Hawkins et al. (1995) as shown in Fig. 3 and Table 2.

Table 2. Comparison of CFD and Experimental data

Sl. No. Position (x/L) Percentage of Error (%) 1 0.035 3 2 0.254 5 3 0.537 10 4 0.94 15



It is observed from Table 2. Near to the supply outlet location the error is less and further distance away from the diffuser the error is more it is due to the faster velocity decay of the jet.

Figure 3 Comparison of velocity profiles with Hawkins et al. (1995) at different x locations

Figure 4 shows the variation of ADPI and DR with cooling load for different values of supply outlet angle. Two different supply outlet angles and three different cooling loads are considered, viz. = 45o, 0o and q = 25 W/m2, 37.5 W/m2, 50 W/m2. It is observed from Fig. 4 that ADPI decreases and DR increases with increases in the cooling load Liu et al. (2016). Hence, the ADPI decreases and DR increase with increase in the heat flux as observed in Fig. 4.

(a)

(b)

Figure 4 Variation of (a) ADPI (b) DR with cooling load for two different supply outlet angle at Tavg = 24 oC

At = 0o the decrease in ADPI and increases in DR is primarily due to the buoyancy force created by the temperature difference between the room temperature and supply outlet temperature overcomes the Coanda effect. Finally, the jet is separated from the ceiling and falls into the occupied zone. This leads to the formation of the stagnation and draft region in the occupied zone. ADPI and DR are found to increase and decreases respectively as the supply outlet angle increase from = 0o to 450.Reason for increase in the ADPI and decrease in the DR may be due to Coanda effect overcomes the buoyancy effect and jet attaches with the ceiling. According to ISO (2005) and ASHRAE standard the draft sensation in the occupied zone is satisfied if DR is less than 10% and ADPI is greater than 80% respectively.

The simulated results for different cooling loads and supply outlet angles have been analysed and corresponding streamline plots, non-dimensionalized velocity and EDT contours are presented in Figs. 5-7. The cooling load has been varied as in practical applications. To meet the required thermal comfort, the supply air velocity and outlet angles are varied at constant room average temperature. Figure 5 shows the streamlines in a longitudinal vertical mid-plane for different values of supply outlet angle and cooling load at constant room average temperature. The streamlines reveal different characteristic regions, viz. primary stream or jet region, recirculating region, stagnant region and separation region. The conditioned air that enters at = 45o forms the primary stream or jet region as shown in Fig. 5(a). The secondary air from the occupied zone and area between the jet and ceiling gets entrained into the primary stream region. The jet gets deflected further upwards and attaches with the ceiling due to Coanda effect. This entrainment of air creates a low pressure area between ceiling and primary stream region which in turn creates a secondary anticlockwise recirculation region at top right corner of the enclosure as shown in Fig. 5(a). Due to entrainment of the surrounding fluid into the primary flow region, the jet decelerates and expands. It strike and moves along the opposite wall. The reverse air stream is formed due to the flow movement across the floor. The entrainment creates a recirculation region in clockwise direction in the entire occupied zone below the primary flow region. Same behaviour is observed for different cooling load values for = 45o. The flow pattern exhibit a different behaviour when the conditoned air enters at = 0o. The Coanda effect is assumed to be negligible due to the buoyancy forces. The entrainment of air into primary stream region decelerates and a favourable pressure gradient is created along the flow. When the jet collides with the opposite wall, reverse flow is observed at top right corner of the room due to adverse pressure gradient. This results in separation of shear layer in downstream of the enclosure and jet falls into the occupied zone. As observed from Figs. 5(b), (c) and (d), the increment in supply air velocity increases the area covered by the recirculation region in the occupied zone.

(a)



(b )

(c)

(d)Figure 5. Streamlines in longitudinal vertical mid-plane for

different supply outlet angle and cooling load (a) o45 , q =

25 W/m2 (b) o0 , q = 25 W/m2 (c) o0 , q = 37.5 W/m2 (d)o0 , q = 50 W/m2.

Figure 6 shows the contours of non-dimensional velocity magnitude in a longitudinal vertical mid-plane for different values of supply outlet angle and cooling load at constant room average temperature. At = 45o, near the supply outlet region, due to high velocity the expansion of jet due to entrainment is limited by the ceiling and uniform velocity distribution is observed in the occupied region and similar behaviour is observed for different cooling loads as shown in Fig. 6(a). At = 0o, based on the cooling load variation, expansion of the jet shows different behaviour. The velocity decay constant of the jet is a strong function of cooling load and values decrease with increase in the cooling load (Hosni et al., 1996). The entrainment is a strong function of turbulent kinetic energy, velocity and diameter at the supply outlet. Increment in supply air velocity and turbulent kinetic energy increases the entrainment of air into the primary stream region. Thus, the expanded jet enters into the occupied zone at a higher cooling load as observed from Figs. 6(b), (c) and (d). Consequently, it creates a draft in the occupied zone.

Figure 7 shows the EDT contours in a longitudinal vertical mid-plane for different values of supply outlet angle and cooling load at constant room average temperature. The contours of EDT are used to discuss about the temperature distribution in the enclosure. At = 45o, 0o the thermal potential core is observed near to the supply outlet region. In the primary stream region the mixing of conditioned air and warmer surrounding air is achieved by the turbulent mixing and molecular diffusion. The cold zone is observed in the primary stream region. In the occupied region uniform temperature distribution is observed in recirculation areas and is not uniform at stagnant areas. The temperature gradient is high in stagnant areas where there is not enough

air circulation and less air velocity. The hot zone is formed in the occupied zone at bottom left corner of the room due to the stagnation of air. Molecular heat diffusion is faster than the molecular momentum diffusion in the stagnation areas due to the Prandtl number of air being 0.7 Zhang et al. (1992). The area covered by the hot zone decreases with increase in the cooling load and cold zone area increases due to the deflection of the jet and enters into the occupied zone.

(a)

(b)

(c)

(d)

Figure 6. Contours of non-dimensional velocity magnitude in longitudinal vertical mid-plane for different cooling loads and supply outlet angles (a) o45 , q = 25 W/m2 (b) o0 , q =25 W/m2 (c) o0 , q = 37.5 W/m2 (d) o0 , q = 50 W/m2.

(a)



(b)

(c)

(d)

Figure 7 Contours of EDT in longitudinal vertical mid-plane

for different supply outlet angle and cooling load (a) o45 ,

q = 25 W/m2 (b) o0 , q = 25 W/m2 (c) o0 , q = 37.5 W/m2 (d) o0 , q = 50 W/m2. Figure 8 shows the stacked column chart for different values of supply outlet angle and cooling load at constant room average temperature. Apparently, it is observed from the Fig. 8 the area covered by cold zone increases with increase in the heat flux. While, the area covered by hot zone initially increases from 25 W/m2 to 37.5 W/m2 and decreases from 37.5 W/m2 to 50 W/m2.

Figure 8. Comparison of dissatisfaction due to EDT for three different heat load condition

The former is due to the faster expansion and velocity decay of the jet and latter is due to the increased in circulation area covered in the occupied zone as observed in Fig 5 (b), 5(c)

and 5(d). The same behaviour is observed for both supply outlet angle as observed in Fig. 8.

CONCLUSIONS Three-dimensional numerical investigations have been carried out to study the flow and thermal characteristics of wall jet diffuser for different supply outlet angles and cooling load at constant temperature difference between the supply air and room average temperature. The streamline plots in longitudinal vertical mid-plane show different characteristic regions, namely, primary stream region, recirculation region, stagnant region and separation region. At higher values of cooling load, expansion of the jet grows while velocity decay decreases at a faster rate. This behaves converse for lower values of cooling load. EDT contours reveal that hot zone appears near stagnant regions and cold zone in the primary stream region. With increase in cooling load, the area covered by the former decreases as compared to the latter.

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