wall-mounted diffuser
The flow in the occupied zone is illustrated in Figure 4.5. This shows how the cold stratified layer of supply air flows into the occupied zone as a radial air movement that covers the whole floor in the room.Figure 4.4 Adjacent zones for wall-mounted diffusers. Diffuser data: Height: H = 0,9 m, Width: B = 0,6 m. Supply air flow: qs = 40 l/s. Under-temperature: Dqs = 6°C.
Figure 4.5 The cold supply air flows radially into the occupied zone.
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Dist. from centre line of
diffuser, \ [m] D iffus er Adjacent zone 0.15 m/s 0.20 m/s 0.5 1.0 1.5 - 0.5 - 1.0 - 1.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Dist. from centre line of
diffuser, \ [m]
Dist from diffuser front, [ [m]
D iffu se r Adjacent zone 0.15 m/s 0.20 m/s Forwards discharge D Sideways discharge E
Dist from diffuser front, [ [m] 0.5 1.0 1.5 - 0.5 - 1.0 - 1.5
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Preface
Measurements of this air movement show that theentrainment in the horizontal flow is very small and it also demonstrates that the depth of the flow is cons- tant in a given situation. The depth of the stratified layer is a function of the Archimedes number
(4.1) or of the ratio
(4.2) where
b volume expansion coefficient = 1/Toz g acceleration of gravity = 9,81 m/s² q oz q s
under-temperature, i.e. difference between the temperature at a height of 1.1 m inside the room and the supply temperature
vs face velocity = qs / As qs supply air flow rate As face area of the diffuser
(height H times width B).
A radial stratified flow with constant depth will have a velocity distribution that is inversely proportional to the distance from the diffuser or from a point (virtual origin) very close to the diffuser. Measurements of the flow from diffusers confirm the theory of this behaviour, see Nielsen (1992) and (2000). Figure 4.6 shows measurements of maximum velocity in the stratified flow along the floor from a wall-mounted diffuser. The cold air has a high initial acceleration due to the buoyancy effect, and the highest velocity is
Figure 4.6 Maximum velocity close to the floor versus distance x from the diffuser. qs = 28 l/s.
obtained at a distance of 0,6 m from the diffuser. The measurements indicate that the velocity vx is
proportional to 1/x for distances larger than ~1 m from the diffuser.
From the above assumption it is possible to find the maximum velocity vx at any distance from the diffuser
when the distance ln, is known from measurements.
The maximum velocity is given by
(4.3) where x is the distance from the diffuser.
The length, ln of the adjacent zone is a function of the
flow rate qs , under-temperature Dqs and the type of
diffuser. The velocity vx will e.g. be equal to 0,075 m/
s at a distance of 4 m if the length ln is 1,5 m. The
maximum velocity will be located 2 to 5 cm above the floor when the temperature difference is large, but it will have a higher location if the temperature difference is small. It is assumed in equation (4.3) that ln, has such a level that the velocity is inversely
proportional to the distance for x larger than ln (this
condition is fulfilled for the measurements in Figure 4.6).
It is also possible to find the velocity distribution in the occupied zone as a function of the volume flow rate and the temperature difference. The maximum velocity is given by
(4.4) where KDr is a function of the flow rate and the under-
temperature (function of Archimedes number). The equation is valid for x ³ 1 - 1,5 m. The length of the adjacent zone, ln , can be found from equation (4.4):
ln = 0,005 qs KDr [m] (4.5) KDr has to be measured for each individual diffuser.
Figure 4.7 shows the variation of KDr for different
types of diffusers. The figure indicates that the first generation of diffusers - located in the upper part of the shaded area had a radial distribution of the flow and a high level of the KDr value. Some diffusers had
a forward discharge of the flow at a low Archimedes number, which in this situation will give a further Ar = b g h (qoz - qs) v2 s (qoz - qs) q2 s vx = 10-3 qs KDr 1 [m/s] x 0,2 0,4 0,6 1,0 2,0 4,0 6,0 0,04 0,06 0,08 0,10 0,20 0,40 0,50 0,60 Y[[m/s] [ [m] ln x vx = 0,2 [m/s]
26
increase in KDr , but the gravity effect turns the flow
into a radial pattern at higher Archimedes numbers. The newest generation of diffusers has a distribution with high velocity parallel to the wall and a lower velocity perpendicular to the wall (sideways dis- charge). This will give the low KDr values shown in
the lower part of Figure 4.7.
Figure 4.7 KDr-values for different types of wall-mounted diffusers for
displacement ventilation. (Note that qp is in l/s).
The upper part of the shaded area in the figure is therefore typical of diffusers with radial/axial distribution of velocity and the lower part is typical of a flat velocity distribution.
Figure 4.7 indicates that KDr is a function of the square
root of the Archimedes number (qoz qs)/qs2. The
maximum velocity vx will therefore be a linear function
of the square root of the Archimedes number and a linear function of the flow rate, see equation (4.4). The KDr value is expressed by the following equation,
see Nielsen (2000)
(4.6)
where
e factor that represents the initial increase in the flow
rate, which is due to entrainment in the downward accelerating flow close to the opening,
bmfactor that adjusts the flow in the direction of the x-axis to the flow profile generated by the diffuser,
see Nielsen (1994 A),
a0the angular width of the radial flow close to the
diffuser
d the depth of the stratified flow defined as the height from the floor to the level where the velocity is vx/2.
The variables are indicated in Figure 4.8. Both e and bm are functions of the Archimedes number.
Figure 4.8 The diffuser in this case has a forward discharge, bm > 1, and a0 is smaller than p. The distance x0 can be ignored in many practical cases. An all-round conventional diffuser has a KDr value of
~ 7 corresponding to d ~ 0,1 m, ao = p and b m ~ 1.
Many of the early diffusers had a radial distribution of the flow with a relatively high level in the symmetry plane as e.g. a bm value of 1,5. This will give a K Dr
value of 11, which is in good agreement with the values given in Figure 4.7. A further increase in the velocity level will be obtained by a design where ao
is smaller than p, which also is typical of an early diffuser design.
A design with sideways discharge, see Figure 4.4, can for example be expressed by a bm value of ~ 0,85,
which gives a K Dr value of ~ 6, which is typical of
the latest generation of diffusers.
KDr = 0,9 e bm a0 d 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 .'U[m-1] θR]θ V TVð °C s² m6 10³
[ ]
[R TV αR Y[ EP! δ HTV27 Example:
Calculation of the adjacent zone for a wall-mounted diffuser
In practice, the crucial question is: How long will the adjacent zone be for a given supply airflow rate? The following example shows the calculation of the adjacent zone for a wall-mounted diffuser with adjustable nozzles behind the front cover, see Figure 4.9.
Figure 4.9 The wall-mounted diffuser of the example. H = 0.45 m, B = 0,54 m. The KDr-value for the diffuser with a given adjustment
of the nozzles is given by:
(4.7) The KDr-value is evaluated from laboratory
measurements, and given by the diffuser manufacturer. From equation (4.7) and (4.5) we can calculate the values of the following table:
Table 4.1 Length of adjacent zone for q oz - q s = 3oC qs KDr ln [l/s] [m-1] [m] 20 8,63 0,86 30 8,14 1,22 40 7,97 1,59 60 7,85 2,35
The obtained length of the adjacent zone may be too long for some applications. It is possible to adjust the nozzles in the diffuser to obtain a flow with more sideways discharge. This adjustment will reduce the
KDr-values to a lower level, and decrease the length
of the adjacent zone.