NOMENCLATURE A Coil heat transfer area, m2 Af2
Coil free cross-sectional area perpendicular to the direction of induced airflow, m2
a, a’, b, c, n, n1, n2 Empirical coefficients cpa
Specific heat capacity of air, kJ/kg K cpw
Specific heat of water (liquid media), kJ/ kg K
K Coil heat transfer coefficient, W/m2 K
K’ Coil heat transfer coefficient times coil heat transfer area, W/K
Kin mi mp mw
Induction coefficient Kin = qi /qp
Mass flow rate of induced air, kg/s Mass flow rate of primary air, kg/s
Water mass (liquid media) flow rate, kg/s
P Chilled beam total cooling capacity, kW Pa
Cooling capacity, provided by primary air, kW
Pw P‘w qi
qp ti1
ti2
tp tr
tw1 tw2 Coil cooling capacity, kW
Coil cooling capacity per beam length, W/m
Induced airflow, L/s Primary airflow, L/s
Induced air temperature entering the coil, °C
Induced air temperature leaving the coil, °C
Primary air temperature, °C Average room air temperature, °C
Temperature of water (liquid media) entering the coil, °C
Temperature of water (liquid media) leaving the coil, °C
∆t Average temperature difference between cooling media in the coil and induced air temperature before and after the coil ,
∆ t =
ƿi ƿs
ti1
+ ti2 2
– tw1
+ tw2 , 2
K
Induced air density, kg/m3 Supply air density, kg/m3
ω Velocity of water (liquid media), measured in the cross-section of the coil pipe, m/s
Coil cooling capacity Referring to figure 1, the following system of equations describes coil heat transfer under steady-state conditions, assuming no condensation on the coil surface. Pw
= mw x cpw (tw2
Pw = K x A x ∆t Pw = mi x cpa
(ti1
– tw1) (3) (4)
– ti2 ) (5) It is not uncommon in design practice
to see the chilled beam water side cooling capacity estimated using single equation 3. Often, the water temperature difference is assumed to be 2.2°C to 3.3°C and the other two equations affecting coil cooling capacity are neglected. It is important to understand that the temperature of water leaving the coil tw2
is a function of several parameters,
including the temperature and velocity of induced air travelling across the coil, as well
48 CIBSE Journal November 2012
particular active beam. As primary airflow increases from 5 to 23 L/s per metre of beam, coil cooling output increases by 70%; however coil cooling output per primary airflow (COPA) becomes three times smaller. Even though a given beam design with a fixed-nozzle configuration may have the same induction coefficient, correlation between coil heat transfer coefficient and primary airflow is not linear (as expressed later in equation 8). As the primary airflow increases, the coil heat transfer coefficient increases at a slower rate than the cooling capacity of primary air. In the previous example, water cooling output increased by 70% while cooling by the primary air (at constant supply air temperature) increases in direct proportion to the primary air flowrate – 360%.
How to increase beam effectiveness Increase cooling coil output while maintaining minimum primary airflow. In this section we present equations governing active beam cooling capacity to better understand their performance.
as the temperature and velocity of the water passing through it. For a given coil, heat transfer coefficient K is a function of all the previously mentioned parameters, and it should be calculated but never assumed. The effectiveness of the active beam is defined by its heat transfer coefficient and coil heat transfer surface area. The higher the KA value, the higher the coil cooling output, the higher the COPA.
•Mass velocity (velocity times density or mass airflow divided by free cross-
•Velocity of water in the coil ω. It is governed by equations of forced
; and
Coil heat transfer coeffcient Coil heat transfer coefficient K for a given chilled beam design depends on:
sectional area of the coil) of induced air travelling across the coil vƿi
convection for air passing through the coil with water (or other cooling media circulating inside the coil) and can be described by the following empirical equation. K =a’ (vƿi
) n1 ωn2 (6) Convective heat transfer coefficient from the
water to the pipe is significantly higher than that from the coil fins to induced air passing through the coil. That is why vƿi
has dominant
effect in equation 6 (where there is turbulent water flow as is normally the case). The authors’ own measurements show that power factor n1 is three to four times higher than n2. Since the coil heat transfer area is constant
for a given beam, a similar equation can be used to calculate heat transfer coefficient times the coil surface area or coil cooling output per degree of temperature difference ∆t. K’= KA =a (vƿi
) n1 ωn2 (6a) The velocity of induced air v, which is
defined by induced airflow per unit length of coil and coil cross-sectional free area, depends on primary airflow qp coefficient Kin
, beam induction and temperature difference ∆t. The first two parameters (in [7]) take into
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90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
Cooling due to water
Cooling due to air
5
10
15
20 Airflow (L/s per beam linear metre)
Figure 2: Contribution of air and water to total cooling capacity of an active beam
25
600 500 400 300 200 100 0
60
Coil output per beam length
45 30
Coil output per primary air used (COPA)
15 5 10 15 20 Airflow (L/s per beam linear metre)
Figure 3: Coil cooling output as a function of primary airflow
25
W/(L/s)
Percentage of total thermal output
watts per metre beam
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