# Case study: Small-office HVAC calculations

The Mortenson headquarters campus in Minneapolis is expanding, and in summer 2017 the company began remodeling and renovating a newly purchased building on the campus. The building is 4 stories with a belowground parking garage. Remodeling started on the 4th floor and will work down to the 1st floor. Included in the renovation is the replacement of old air handling units. The HVAC system is variable air volume (VAV) with reheat. Each floor is approximately 15,000 gross sq ft. For this example, calculations for the 4th floor will be used to illustrate Ventilation Rate Procedure (VRP) calculations.

Step 1: Commit to a procedure. In this case, VRP was selected.

Step 2: Determine if Minneapolis had particulate (such as PM10 or PM2.5) and ozone concentrations noncompliant with the standard. As referenced in Informative Appendix F, the U.S. Environmental Protection Agency’s Green Book was used along with Figure F-1 to determine that no contaminants listed in ASHRAE Standard 62.1: Ventilation for Acceptable Indoor Air Quality, Section 6.2.1, exceeded the standard and that no additional contaminants not addressed in 6.2.1 exceeded the standard. As a result of the investigation, no additional filtration was required.

Step 3: Zone calculations. For the Mortenson remodel, zones were determined by orientation, use, and size. Most of the spaces are open-office space with corridors, additional spaces included private offices, two conference rooms, and a break room. Each zone is measured to determine the zone floor area (A_{z}). With zones identified and overlaid on a furniture plan, it is easier to determine and support the zone population (P_{z}). If the furniture layout is not available, default occupant densities can be used. They are outlined in Table 6.2.2.1, which also prescribes values for the people outdoor-air rate (R_{p}) and area outdoor-air rate (R_{a}). With this information, breathing-zone outdoor airflow (V_{bz}) can be calculated using equation 6.2.2.1.

V_{bz} = R_{p} x P_{z} + R_{a} x A_{z }

Using Zone 4-1 as an example. P_{z} = 9, A_{z} = 850. It is office space and from Table 6.2.2.1: R_{p} = 5 and R_{a} = 0.06. If the furniture layout is not available, and default values from the table are used, the occupant density would be 4.25 people. In this case, using the default values would result in potentially underventilating.

V_{bz} = 5 x 9 + 0.06 x 850

V_{bz} = 96 cfm

There are many ways for engineers to configure air distribution into each zone. Each distribution configuration has a different efficiency at delivering outdoor air to the breathing zone. Because of this, ASHRAE has provided Table 6.2.2.2, the zone air-distribution effectiveness table, that either penalizes or rewards systems for their efficiency. For this example, the system will be providing "ceiling supply of warm air 15oF or more above space temperature and ceiling return," which has a zone air-distribution effectiveness (E_{z}) of 0.8. This is typical for traditional overhead VAV systems. To account for different efficiencies, the zone outdoor airflow (V_{oz}) is determined using equation 6.2.2.3:

V_{oz} = V_{bz}/E_{z }

For Zone 4-1

V_{oz} = 96/0.8

V_{oz} = 120 cfm

If Zone 4-1 is a single-zone system, the system outdoor air intake flow could be calculated using equation 6.2.3:

V_{ot} = V_{oz }

V_{ot} = 120 cfm.

If the system is a dedicated outdoor-air system or 100% outdoor-air system, the designer would run the same calculation on all 16 zones and then use equation 6.2.4:

V_{ot} = ^{Σ}all zones^{Voz }

Because the system in this example is a multiple-zone recirculating system where an air handling unit provides a mixture of outdoor air and recirculating air to more than one zone, Section 6.2.5 must be followed.

For this system, there are several more calculations that must be made. The first is calculating the primary outdoor-air fraction (Z_{pz}) for each zone. This is the primary airflow at the design condition analyzed (summer or winter and should be based on design conditions at normal operations). V_{oz} has been calculated above and the minimum primary airflow V_{pz} is determined via HVAC load calculations.. To calculate the primary outdoor-air fraction Z_{pz}, use equation 6.2.5.1: Z_{pz} = V_{oz}/V_{pz }

In the Zone 4-1 example calculation, the VAV unit is sized for 1,890 cfm in cooling with a minimum of 500 cfm supplied to the space. Thus, V_{pz} is equal to 500 cfm.

Z_{pz} = 120/500

Z_{pz} = 0.24.

The zone’s primary airflow fraction is then used in another ventilation efficiency category: system ventilation efficiency (E_{v}). Table 6.2.5.2 or Normative Appendix A can be used to find E_{v} values. Using Standard Table 6.2.5.2, the Z_{pz} value of 0.24 is equal to an E_{v} value of 0.92.

This series of calculations is run for every zone in the system. While important to understand how the calculations are run, this is where spreadsheets and online calculators become helpful. It will be necessary to investigate each zone individually for optimizing system ventilation efficiency, as the zone with the lowest E_{v} becomes the "critical zone."

When every zone has been calculated, occupancy diversity (D) should be calculated. Diversity allows for the fact that the actual number of people using the space at any given time will be less than the peak occupancy in each zone. The 4th floor in the Mortenson building is intended to serve a population (P_{s}) of 70 team members. When all zone populations are added up, the space could serve 93 team members. Diversity is calculated using Equation 6.2.5.3.1:

D = P_{s}/ ^{Σ}all zones^{Pz }

D = 70/93

D = 72.9%

At this point, the "uncorrected" outdoor-air intake (V_{ou}) can be calculated. In mixing systems, uncorrected outdoor-air intake allows for diversity across the system. For the Mortenson 4th floor, the sum of all (R_{p} x R_{z}) is 480 cfm and the sum of all (R_{a} x A_{z}) is 709 cfm. Using this information, V_{ou} is calculated using Equation 6.2.5.3:

V_{ou} = D ^{Σ}all zones (R_{p} x P_{z}) + ^{Σ}all zones(R_{a} x A_{z})

V_{ou} = 0.729 (480) + (702)

V_{ou} = 1,052 cfm

Using the spreadsheet created showing all zone information (Table 1), identify the critical zone, zone with the lowest E_{v}, as noted earlier. In this example, Zone 4-2 has the lowest E_{v} at 0.64.To determine the outdoor-air intake (V_{ot}) for a multizone system, the zone with the lowest system ventilation efficiency (E_{v}) will be used..

Outdoor-air intake (V_{ot}) for a multizone system is calculated using Equation 6.2.5.4:

V_{ot} = V_{ou}/E_{v }

V_{ot} = 1,052 cfm / 0.64

V_{ot} = 1,643 cfm

What this means is that because there is a zone with a lower ventilation efficiency, the remainder of the system is penalized for it. If the zone’s primary airflow to Zone 4-1 is increased to 500 cfm, the value for Z_{pz} goes to 0.36 and the E_{v} becomes 0.80. This would reduce system airflow V_{ot} to 1,331 cfm, which is a 19% reduction in required outdoor airflow. Depending on system type, climate, and occupancy, this reduction in outdoor air should directly correlate to reduced energy costs. However, raising minimum flow rates to certain zones can increase the need for reheat in VAV systems. This is a great study to perform, but it is not included in this article.

Another option for calculating E_{v} is using appendix A, and it must be used when Table 6.2.5.2 values are not used. The Appendix A calculations are not included here but were run for comparison. The calculated value for E_{v} using appendix F is 0.85. This resulted in a V_{ou} value of 1,235 cfm. It is up to each engineer running outdoor-air calculations to decide which calculation method is right for a project. With the advent of available calculators and spreadsheets, it is reasonable for engineers to quickly evaluate E_{v} using either method and then determine which E_{v} value they want to use in design.

Julianne Laue is the director of building performance at Mortenson. She is a 40 Under 40 award winner, and a member of the Consulting-Specifying Engineer editorial advisory board.