Temperature Measurement; the Impact of Mass Flow Rate on Mixed Air Temperature

One of the questions I often ask in classes I teach on
commissioning and controls is as follows:

If you entered an air
handling unit that was experiencing stratification in the mixed air
plenum and measured the temperature in the center of each filter
and averaged the results, would the answer be the same as the one
you would get if you measured the temperature of the air after it
was completely mixed down stream of the filter bank?

The answer is “Not
necessarily” and is illustrated in the figures below.

Filter Bank Data

    

Upper Left
Filter                                                             
Lower Right Filter

Figure 1 – A filter bank
with significant temperature stratification between the upper left
and lower fight corner (outlined in red and magnified) but fairly
uniform air flow.

Filter Bank Data

    

Upper Left
Filter                                                            
Lower Right Filter

Figure 2 – The same
filter bank as in Figure 1 but with a non-uniform flow
profile.

Figure 1 illustrates a
filter bank with significant temperature stratification between the
upper left corner and lower right corner but with a fairly uniform
flow rate across the filter bank. The second figure illustrates the
filter bank with the same temperature stratification combined with
a very non-uniform flow profile.

The non-uniform flow profile
is the key to the reason that the answer to the question I pose is
“Not necessarily”. This is because the temperature of the air after
it is completely mixed is a function of both the temperature and
the mass flow rate of the air through each individual filter
element measured in the temperature traverse. Filters with air
streams at higher velocities (i.e. more air flow) will have more
influence on the mixed temperature than filters with low
velocities/less air flow.

Think of it this way; If I
dump 1 gallon of water at 50°F into a tank with 99 gallons of
water at 100°F, the result will not be 100 gallons of water at
75°F because of the mass of water at 100°F relative to the
mass of water at 75°F.  A similar situation occurs when
air that is stratified both in terms of temperature and mass flow
rate becomes thoroughly mixed; the temperature of the air
streams with more mass will predominate. The result for the two
filter banks illustrated in Figure 1 and 2 is as illustrated in the
tables below.

Total area for the filter
bank (sum of individual element areas) – 80 sq.ft.
Total flow for the filter bank (sum of individual elements) –
36,064 cfm
Average velocity for the filter bank (average of individual
elements) – 451 fpm
Average temperature (average of individual temperature readings) –
58 °F
Mass weighted average temperature (individual temperature readings
times related flow divided by total flow) – 57.9 °F 

Table 1 – Summary for the
filter bank illustrated in Figure 1

Total area for the filter
bank (sum of individual element areas) – 80 sq.ft.
Total flow for the filter bank (sum of individual elements) –
35,776 cfm
Average velocity for the filter bank (average of individual
elements) – 447 fpm
Average temperature (average of individual temperature readings) –
58 °F
Mass weighted average temperature (individual temperature readings
times related flow divided by total flow) – 61.1 °F

Table 2 – Summary for the
filter bank illustrated in Figure 2

These results can have significant implications in terms of the
performance and problems that might be experienced in mixed air
plenums serving systems that see extremely low outdoor air
temperatures. More on this will follow in a subsequent post.

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