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Modeling the performance of single-duct VAV systems that use Fan Powered terminal units.


The purpose of this study was to model the operation of the Single Duct Variable Air Volume (SDVAV) systems that used Fan-Powered Terminal Units (FPTU). The objective of this paper is to describe the system model and to serve as a reference for other papers that detail the operation of the system when series or parallel type fan powered terminal units are used.

Variable Air Volume (VAV) systems maintain zone comfort by varying the amount of primary air that is delivered to conditioned spaces. The central cooling system includes a fan and cooling coil that supply pressurized and conditioned air to the primary distribution ducts. The central fan is usually referred to as the primary fan while the air that is conditioned by the cooling coil is referred to as primary air. Primary air is supplied to the conditioned space by a VAV terminal unit that regulates the amount of primary air supplied to the zone.

Figure 1 shows a SDVAV system using five FPTU. For this project, a three zone system model was developed and used to determine a matrix of test points that were then used to perform laboratory verification of the model. After the three zone model was verified it was expanded to five zones and used to evaluate the operation of a building at five different weather locations around the United States. The three zone and five zone models used the same methodology for all calculations with the exception of error corrections that were made as a result of the laboratory verification process. The verification of the model is described in a related paper (Bryant et al. 2009).



The system simulation procedure began with the calculation of zone level conditions followed by the return air calculations, the introduction of fresh air, pre-heat coil process and finally the primary fan and cooling coil calculations. The zone level calculations were dependent upon the type of FPTU installed in the zone. For the purpose of describing the system model, the zone level calculations will be treated as a "black-box" model that provides known values for the parameters related to the operation of the conditioned space. Using the known space parameters, the rest of the system calculations may be performed.

After the zone-level return air calculations were completed, the mixed return-air conditions were calculated following the introduction of fresh air. Next, the air properties leaving the pre-heat coil were estimated and entering and leaving conditions for the primary fan were calculated. The properties of the air leaving the primary cooling coil were assumed to be the same as the primary air entering the SFPTU. At each step along the flow path, the temperature and moisture content of the air were calculated. In the cases where air streams were mixed, the mixed air properties were calculated.

Figure 2 shows a flow diagram that identifies the calculation sequence used in the simulation program. The following sections detail the calculation procedures used in the model.


It was not required that the inlet flow valve position at each FPTU be predicted accurately by the model for a given set of duct conditions. The calculation procedure covered below assumed that the VAV valve would adjust as required to meet space conditions. This assumption was verified during laboratory tests and found to be reasonable. The model description will begin with the zone level calculations.


The zone calculations were performed based on the type of FPTU installed in the zone. To be able to predict the behavior of the system, this model had to accurately predict upstream static pressure and primary air flow requirements for known space loads.

The parameters determined by the zone level calculations consisted of the following:

1. The amount of primary air required by the zone - this included any air that had to be supplied to make up for leakage from the FPTU and between the FPTU and the space.

2. Any heat required to maintain space conditions including reheat for over cooling and space heating.

3. The upstream static pressure required by the primary fan.

4. The temperature of the return air from the zone.


Temperature, absolute humidity, and flow rate of the return air at the zone level were determined by the model based on the FPTU type and the zone sensible and latent loads. The properties for the system return air were evaluated by performing an energy and mass balance on the return air duct. Equation 1 was used to calculate the return air mixed air temperature and was based on an energy balance of the return air stream (ASHRAE 2005).

[T.sub.ra] = [[[n.summation over (i = 1)] [V.sub.i][T.sub.i]]/[[n.summation over (i = 1)] [V.sub.i]]] (1)

Similarly, Equation 2 was used to calculate the mixed return air humidity ratio based on a mass balance of the return air duct.

[[omega].sub.ra] = [[[n.summation over (i = 1)] [[omega].sub.i] [V.sub.i]]/[[n.summation over (i = 1)] V]] (2)


The properties of the mixed air after the exhaust of some return air and introduction of fresh air were based on energy and mass balances similar to the calculations for the air streams entering the return system from the zones.

The mixed air temperature after the exhaust/fresh air intake was calculated using Equation 3.

[] = [XT.sub.oa] + (1 - X) [T.sub.ra] (3)

In Equation 3, the fraction of air introduced into the return air system is the same as the fraction of the return air that was exhausted from the system. The humidity ratio of the mixed air stream after the exhaust and fresh air intake was calculated using Equation 4:

[[omega]] = [X[omega].sub.oa] + (1 - X) [[omega].sub.ra] (4)


The return air entered the pre-heat coil as mixed air after fresh outside air was introduced into the system. If the temperature of the mixed air was too low after the introduction of the outside air, then heat was added. The required amount of heat was determined using equation 5. If the temperature of the return air was above the minimum entering air temperature for the primary fan, then no heat was added and the air entering the fan was the same as the mixed air temperature. The humidity ratio did not change as the air passed through the pre-heat coil.

[] = 1.08V ([T.sub.min] - []) (5)


The increase in the temperature of the air as it passed through the fan was calculated from Equation 6 where the value of Q was the work done on the air by the fan. The heat added to the air (Q) was calculated using Equation 8 which was developed from manufacturer's literature.

[] = [] + [[]/1.08 V] (6)

Equation 7 is a fan model that was developed from manufacturer's data for primary fan air flow as a function of the fan speed in RPM and static pressure. Coefficients used in this equation are given in Table 1.
Table 1. Coefficients for Equation 7

           Coefficient             English Units

[a.sub.1]    -1227.76              [ft.sup.3]/min
[a.sub.2]    -1610.45          [ft.sup.3]/min-in.w.g.
[a.sub.3]       3.047      [ft.sup.3]/min-[(in.w.g.).sup.2]
[a.sub.4]       3.786            [ft.sup.3]/min-rpm
[a.sub.5]    -0.00017        [ft.sup.3]/min-[rpm.sup.2]
[a.sub.6]       0.302        [ft.sup.3]/min-in.w.g.-rpm
[a.sub.7]    -9.8E-07   [ft.sup.3]/min-[(in.w.g.-rpm).sup.2]

           Coefficient            SI units

[a.sub.1]    -252.2            [m.sup.3]/min
[a.sub.2]    -410.2           [m.sup.3]/min-Pa
[a.sub.3]     0.610       [m.sup.3]/min-[Pa.sup.2]
[a.sub.4]     0.610          [m.sup.3]/min-rpm
[a.sub.5]   -.000003      [m.sup.3]/min-[rpm.sup.2]
[a.sub.6]     0.013         [m.sup.3]/min-Pa-rpm
[a.sub.7]   -1.7E-09    [m.sup.3]/min-[(Pa-rpm).sup.2]

The fan speed was determined first from the required combination of air flow and primary static pressure. The required air flow was the total primary air required to serve all of the zones. The primary static pressure was the highest static pressure that was required to serve any one of the zones.

V = [a.sub.1] + [a.sub.2]P + [a.sub.3][P.sup.2] + [a.sub.4]S + [a.sub.5][S.sup.2] + [a.sub.6]PS + [a.sub.7][P.sup.2][S.sup.2] (7)

The model also included facilities for setting the primary static pressure to either a specific value, a minimum value, or to a base value. The minimum static pressure setting would not allow the primary static pressure to drop below the specified value. The base value parameter was used to establish a base primary static pressure to which the highest zone static pressure was added. The minimum and base static pressures were used to model losses through the primary coil as well as filters and primary duct pressure drops. The specific static pressure setting was used to model systems that maintain a constant primary static pressure.

Equation 8 was then used to calculate the amount of power consumed by the fan using Equation 7 iteratively to solve for the required fan speed.

[] = 746 [(S/1631).sup.2] (1/efficiency) (8)


The temperature of the air entering the cooling coil was calculated by adding the temperature rise across the fan to the temperature of the air leaving the pre-heat coil. The sensible cooling load at the cooling coil was calculated using Equation 9.

[Q.sub.ccsen] = 1.08V ([] - []) (9)

The latent load on the primary cooling coil was calculated using Equation 10.

[Q.sub.cclat] = 4840 V ([[omega]] - [[omega]]) (10)

4840 = conversion factor with units of Btu-min-lbair/[ft.sup.3] - hr-[lb.sub.water]. The S.I. equivalent is 46.05 kW-min-[kg.sub.air]/[m.sup.3] -[kg.sub.water]

The total load on the cooling coil was the sum of the sensible and latent loads.


The cooling plant was modeled as a simplified DX cooling system where the efficiency (EER) decreased linearly as a function of the increase in the outdoor temperature. A starting EER was based on 95[degrees]F (35[degrees]C) outdoor temperature and for every 10[degrees]F (18[degrees]C) that the temperature was over 95[degrees]F (35[degrees]C), the EER dropped by 1 point. The EER used for the model was an input to the model spreadsheet and was not related to any specific piece of equipment or manufacturer.


The model verification is detailed in another paper (Bryant et al. 2009) and will only be covered briefly in this paper. A three zone system test stand was designed and constructed to support an air distribution system consisting of three SDVAV zones. The test stand was built with a primary air plenum supplying air to three separately controllable duct systems which served as the three zones. Measurements were taken of the primary, induced, and supply air stream temperatures. Additional measurements consisted of the primary and induced air relative humidity, upstream, downstream and flow sensor static pressure, silicon controlled rectifier (SCR) voltage, terminal unit fan power, and the power supplied to a duct heater that was installed in the supply air streams for each zone. Conditioned air was supplied to the primary air plenum and room air was available to the induction ports. The air flow rates and pressures were controlled with actuators that modulated control dampers. The amount of primary air that passed through the terminal unit was controlled by an actuator that opened and closed a damper located in the primary inlet port of the terminal units. The speed of each terminal unit fan was adjusted by an actuator attached to a voltage controller.


After the model accuracy was laboratory verified, it was used to evaluate the performance of SDVAV systems with both series and parallel FPTU. The model showed that the energy exchanges in the system occurred in four key processes: 1) zone operation, 2) primary cooling coil, 3) primary fan, and 4) introduction of fresh air. The model showed that the operation of the zones had a significant impact on the operation of the primary fan. The processes related to the energy interactions at the primary coil and during the introduction of fresh air were not studied in detail as a part of this project.

The processes related to the zone operation were the primary focus of this study but the zone operation had such a significant impact on the system that the operation of the primary fan had to be included in the study of the FPTU. Figure 3 shows the primary air flow rate of typical parallel and series FPTU as a function of space loads handled by the FPTU.


Figure 3 shows the primary air flow rate as a function of the zone sensible load for Series and Parallel FPTU. This figure also shows the minimum air flow rate required to meet the space sensible load. As the zone load changes the primary air flow varies from maximum to minimum. The minimum flow rate for the FPTU was set at 20% of maximum. Once the space load dropped below 20% of the maximum load, the primary air flow rate was maintained at 20% of the maximum flow rate.

Primary air leakage was common for all of the parallel FPTU tested in the laboratory. The flow rate for the parallel FPTU shown in Figure 3 did not include any leakage which is why the parallel units performed similarly to the theoretical minimum required air flow rate. The leakage from the parallel units was from the seams of the pressurized mixing chamber as well as from the back-draft damper. The leakage of parallel FPTU is discussed in detail in another paper that describes the zone model used with the system model (Davis et al., 2009). The series FPTU did not leak but it is a very realistic possibility that if a building management system is not properly tuned, more supply air can be driven into the mixing chamber than the FPTU fan can supply to the space. With the over pressurized condition, the series FPTU would use more air at part load conditions than shown in Figure 3.

Figure 4 shows the primary air flow rate as a function of zone sensible load for parallel FPTU with leakage rates of 0%, 10%, and 20%. Figure 4 also includes the primary air flow rate for a series FPTU. The primary air flow rate increases for all operating conditions when parallel units leak. Figure 4 also shows that the primary air requirements for a parallel FPTU with a leakage rate higher than 10% is equal to or greater than the primary air required for a series FPTU where the air flow rate is not higher than the terminal unit fan operating point.


Figure 5 shows the primary static pressure as a function of zone sensible load for both series and parallel FPTU. The parallel FPTU shown in Figure 5 had a leakage rate of 0%. This figure shows that the primary static pressure requirements for the series FPTU is always lower than the primary static pressure required for the parallel FPTU. It also shows that when the zone sensible load reduces to the point that the parallel FPTU fan is activated, the primary static pressure is forced to increase in order to maintain minimum primary air flow rate. The impact on the system is that the system primary static pressure is increased and all air flow through the system must be moved against the higher static pressure. The result is that the maximum static pressure required by any of the zones is the minimum static pressure that has to be supplied by the primary fan.


Figure 6 shows the primary static pressure as a function of zone sensible load for parallel FPTU with leakage rates of 0%, 10% and 20%. Figure 6 also includes the primary static pressure for a series FPTU. This shows that the increased primary air flow required as a result of the leakage rate from the parallel FPTU results in an increase in the primary air static pressure. The leakage rate also impacts the primary static pressure required at minimum load when the parallel unit fan is activated. Figure 6 shows that for all operating conditions, the primary static pressure required by the series FPTU is lower than the pressure required by the parallel units.



This paper had two objectives: 1) describe the system model, 2) serve as a reference for the papers that describe the zone models and the impact on the system from the type of FPTU used in the zone.

The model description detailed the performance calculations for components used in a typical SDVAV system with FPTU. The calculations started with the zone loads and proceeded through the entire system until the air properties were known for all air streams in the system.

The model was verified by using it to predict duct conditions and control point settings for a variety of operating points that were then replicated in an experimental test rig. A laboratory test stand was built and operated using this matrix of test points determined with the SDVAV model with FPTU (Bryant et al. 2009). At each test point, the supply temperature predicted by the SDVAV model was compared with the actual data from the test stand. The measured supply temperatures were found to agree with the predicted supply temperatures within the uncertainty of the experimental measurements thus verifying the accuracy of the model over the full operating range of the SDVAV FPTU system model. For a complete description of the uncertainty analysis, please refer to Bryant et al. 2009.

The impact on the primary fan because of leakage from the parallel FPTU has a negative impact on the performance of air conditioning systems that use these type terminal units. The impact on the primary fan at minimum loads due to the activation of the terminal fans has a negative impact on the operation of the systems that use parallel FPTU. It cannot be concluded from the data presented in this paper that either the series or parallel based systems are the "best" system to use in a given application. The performance of both systems are compared in related papers.


This work was part of a project funded by ASHRAE under RP-1292 and we would like to thank the project monitoring subcommittee of TC 5.3 and the manufacturers they represent for their support during the project. Several manufacturers donated terminal units for use in this study. Through cooperative ventures such as these, ASHRAE research funding can be utilized to the fullest. We appreciate the contributions from these industry leaders.


[a.sub.1] - [a.sub.7] = coefficients used in Equation 7

P = primary fan static pressure, in. w.g. (Pa)

[Q.sub.cclat] = latent cooling coil load, Btu/hr (W)

[Q.sub.ccsen] = sensible cooling coil load, Btu/hr (W)

[] = primary fan power, Btu/hr (W)

[] = sensible energy added at preheating coil, Btu/hr (W)

S = fan speed, RPM

[] = temperature of the air entering the coil, [degrees]F ([degrees]C)

[T.sub.i] = temperature of the air returned from zone i, [degrees]F ([degrees]C)

[] = mixed air temperature before it enters the terminal unit fan, [degrees]F ([degrees]C)

[T.sub.min] = minimum temperature leaving preheat coil, [degrees]F ([degrees]C)

[T.sub.oa] = temperature of the outside air, [degrees]F ([degrees]C)

[] = temperature of the primary air, [degrees]F ([degrees]C)

[T.sub.ra] = temperature of the return air, [degrees]F ([degrees]C)

V = volumetric air flow rate, [ft.sup.3]/min ([m.sup.3]/min)

[V.sub.i] = volumetric air flow rate, [ft.sup.3]/min ([m.sup.3]/min)

[[omega].sub.i] = humidity ratio of the ith zone return air, [lb.sub.moisture]/[lb.sub.air] ([kg.sub.moisture]/[kg.sub.air])

[[omega]] = mixed air humidity ratio, [lb.sub.moisture]/[lb.sub.air] ([kg.sub.moisture]/[kg.sub.air])

[[omega].sub.oa] = humidity ratio of the outside air - [lb.sub.moisture]/[lb.sub.air] ([kg.sub.moisture]/[kg.sub.air])

[[omega].sub.ra] = return air humidity ratio, [lb.sub.moisture]/[lb.sub.air] ([kg.sub.moisture]/[kg.sub.air])

[[omaga]] = primary air humidity ratio, [lb.sub.moisture]/[lb.sub.air] ([kg.sub.moisture]/[kg.sub.air])

X = mass fraction of fresh air added to the return air, expressed as a fraction


ASHRAE. 2005. ASHRAE Handbook - Fundamentals, Chapter 30, Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Bryant, J., Davis, M.A., O'Neal, D.L., and Cramlett, A.: "Experimental Verification of a Three Zone VAV System Model Operating with Fan Powered Terminal Units (RP-1292)", ASHRAE Transactions 08, in publication.


ASHRAE. 1996. ANSI/ASHRAE Standard 130, Methods of testing for rating ducted air terminal units. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

McQuiston and Parker, Heating, Ventilating, and Air Conditioning, 5th ed., 2005

Michael A. Davis

Associate Member ASHRAE

Dennis L. O'Neal, PhD, PE


John A. Bryant, PhD, PE


Andrew Cramlet

This paper is based on findings resulting from ASHRAE Research Project RP-1292.

Michael A. Davis is a research engineer with and John A. Bryant is an associate professor in the Mechanical Engineering Program at Texas A&M University at Qatar. Dennis L. O'Neal is a professor in and head of and Andrew Cramlet is a graduate student in the Mechanical Engineering Department at Texas A&M University, College Station, TX.
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Title Annotation:variable air volume
Author:Davis, Michael A.; O'Neal, Dennis L.; Bryant, John A.; Cramlet, Andrew
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2009
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