# Central Recirculation System

Typically, when central recirculation is used the contaminant in the supply air is the main source. This is not the case for industrial use, where the main source is in the ventilated room. This usually results in the concentration being somewhat higher when using recirculation than when not using it. Figure 8.1 outlines the ventilation system, the contaminant source, and the cleaning system. Air cleaner FIGURE 8.1 Model of a central recirculating system used for calculating the connection between contaminant concentrations, airflow rates, contaminant source strength, qm, and air cleaner efficiency, 75. csup is the concentration in the supply (outside) air, c is the concentration in the room, c„t is the concen­tration in the returned air, qairtot is the total flow rate through the room, k is the ratio between recircu­lated airflow rate and total air flow rate, T is the time constant for the room, and V is the room volume.

In the figure the two flows (supply—exhaust and recirculated) are sep­arated for clarity. Normally they are merged on both the supply and ex­haust side.

The following differential equation (or something similar), derived from a mass balance for the room, is solved to find the correlation between flow rates, source rate, contaminant concentrations, cleaning efficiency, and time.

0 — ^cO^airtot^s ^c^airtot^C ^ — V) Qm ~ ^airtot^ 7 (8.1)

Where the recirculation ratio, kc, is defined as

— •/airier

^airtot

And

Kf is always less than 1

C7airret1S fhc return airflow rate, m V

^airtot’s the total flow rate through the room, m V1

Cs is the concentration in the supply air, mg m-3

C is the concentration in the room, mg m~3

7] is the efficiency of the cleaner (0-1)

Qm is the source rate, mg s-1

V is the volume of the room, m3

T is time, s

It is possible to have a separate recirculating system in addition to the general ventilation system; then rhere is no restriction on the flow rate. This case is the same as a recirculating local exhaust system (see below)

By assuming the supply air concentration to be zero, since usually there are quite different contaminants in the outside air and from the source, and that the initial concentration also is zero, the time-dependent solution is the following,

.. __ w 1 ^ j — + K‘ ) ( S ^)

^airtot (1 V)

Where T is the time constant for the room, s, equal to V/qainov

By assuming a steady state and since the sum of the supply and return flow rates is equal to the total flow rate through the room, it is possible to ma­nipulate this equation to get the following, where gairsup is the supply airflow rate, m3 s-1:

C =————- 2m————————————————— . (8.3)

*7airsup aitietV

This equation shows clearly the influence of the recirculated air. With a source rate of qm and a general ventilation flow rate of gairsup the concentration is qm/<?alI. sup — The addition of recirculated air corresponds to an increase of the supply flow rate by the amount q3lrnt times T] and decreases the concentration. On the other hand, if a part of the original supply air without recirculation (that is, the total flow rate before recirculation is equal to gairsup + q^mn) IS re_ circulated, the concentration will increase.

Another solution to the differential equation for steady state is the follow­ing, where the concentration in the supply air, cajrsup, is included:

C=-2jd——————————————————————————- x (8.4)

4<nrtot (l-Kc + K^TjJ (1 — Kc + KcV)

This equation is the same as the solution for the steady state without contami­nant in the supply air, but with an added multiplication term (the third part on the right) that shows the influence of the recirculation.

Another equation that includes the initial concentration and the concen­tration in the supply air and the mixing factor has been published: 32

C =- c e-fl<7.irSup + + /^upi/airs. ip + qm: x / j _ e~M*m *

‘ f(‘7 airsup ^l^airret)

(8.5)

Where c0 is the initial concentration at time zero, mg m~3, and f is the mixing factor, here defined as the portion of the supply airflow that is completely mixed with room air.

This equation can also be used for steady-state conditions, when the expo­nential terms are taken away and for complete mixing when f is set to 1.