Experimental verification of a three zone VAV system model operating with fan powered terminal units.
Variable Air Volume (VAV) systems maintain comfort by varying the amount of primary air delivered to conditioned zones in a building. Primary components for VAV systems typically include a fan and cooling coil that supply pressurized and conditioned air to the primary distribution ductwork. This fan is referred to as the "primary" fan and the conditioned air is the "primary" air. A VAV terminal unit regulates the amount of primary air supplied to the zone in response to zone cooling or heating loads.
This study focused on the operation of a Single Duct Variable Air Volume (SDVAV) system using Fan Powered Terminal Units (FPTU). Figure 1 shows a SDVAV system using FPTUs serving five zones in a building. The primary fan pressurizes the duct system and controls static pressure supplied at each FPTU. Static pressure control for the primary fan is typically governed by the zone with the greatest need for cooling (zone cooling load).
[FIGURE 1 OMITTED]
There are two common fan powered terminal units -Series and Parallel. Both of these FPTU types have small fans built into the terminal unit. When the terminal unit fan is operating it draws air from the zone return air plenum and supplies the space with a mixture of cool primary and warm plenum (return) air.
Series FPTUs have a small internal fan that works in series with the primary system fan. Conversely, the parallel FPTU has its fan arranged to operate parallel to the primary fan. The control of either of these units is different too. Series units typically run continuously, supplying a constant volume of air to the space. Even if the primary VAV inlet valve to the FPTU is at minimum, the series unit still delivers a fixed volume of air. Minimum inlet valve setting also corresponds to minimum cooling load or initiation of heating mode. A series FPTU will first use warmer plenum air for heating through an induction port built into the unit. If additional heat is needed for the zone, an electric or hot water reheat coil at the discharge of the FPTU will be activated. The parallel FPTU fan operates only if the zone it serves needs heat. In heating mode, the parallel FPTU first draws warmer air from the return plenum and if the zone controller continues to need heat, reheat (either electric or hot water) can be added to the airstream.
Experimental work on FPTUs resulted in the development of characteristic performance models for airflow, power, and pressure drop through the FPTU (Furr et al. 2008).
This paper will focus on the methodology used to model a three zone VAV system operating in a building and the comparison of that model with experimental results from laboratory testing of a complete three zone VAV system operating with fan powered terminal units.
For this study, VAV FPTUs were supplied from three different manufacturers. The FPTU sizes and ratings were selected by the manufacturers to represent the most common units typically used in current VAV system design. The manufacturers supplied one 8 inch (203 mm) and one 12 inch (305 mm) size in each of the series and parallel FPTUs. A three-zone VAV system configuration evolved from this selection of FPTUs because incorporating more zones would only have duplicated the use of a particular FPTU model.
Figure 2 shows the layout of a generic three zone office building model used to generate heating and cooling load data. The development and application of the building model will be described in the following section.
[FIGURE 2 OMITTED]
The building model consisted of commonly defined zones with exterior exposures covering a range of loads resulting from weather and solar effects. To match the three zone VAV system configuration, the North, South, East, and West zones were combined into North - East and South - West zones. The interior, or core zone, would be dominated by internal thermal loads. The building was a single story rectangular structure with a footprint of 122.5 x 122.5 ft (37.3 x 37.3 m). The perimeter zones had 1,612 [ft.sup.2] (149.8 [m.sup.2]) of floor area and 50% glass walls while the core zone had 8,556 [ft.sup.2] (794.9 [m.sup.2]). The perimeter zones had walls with a U-Factor of 0.46 Btu/hr/[degrees]F/[ft.sup.2](2.6 W/[m.sup.2]/[degrees]C) and a solar heat gain coefficient of 26%. The wall insulation was R-13 (2.6 [m.sup.2]K/W) and the roof insulation was R-15 (2.64 [m.sup.2]K/W). The cooling loads due to people in the building were calculated using a factor of 275 [ft.sup.2] (25.5 [m.sup.2]) per person. The lighting and equipment loads were 1.3 W/[ft.sup.2] and 0.75 W/[ft.sup.2] (14 W/[m.sup.2] and 8.1 W/[m.sup.2]) respectively.
The building was operated on a typical office schedule for the entire year. Hourly sensible and latent space loads were calculated for all zones for the entire 8,760 hours in a year using TMY weather data for five locations: Chicago, Houston, New York, Phoenix and San Francisco (NREL 1995). These climates were chosen because of the variety in range of peak summer and winter ambient temperatures, the range of latent loads during the cooling months, and number of hours in cooling or heating mode during the year.
Figure 3 shows the numbers of hours at an average temperature over the course of a year for each city. Each city shows that a significant number of hours in the year are at temperatures other than peak heating or cooling temperatures. The large variation in high and low temperatures, time spent at given temperatures (cooling or heating loads), and span of temperature extremes are evident for these cities. A building "moved" to each of these geographical locations would have significantly different heating and cooling load profiles. The load variations represented with these locations would permit complete characterization of the three zone VAV model under different operating conditions.
[FIGURE 3 OMITTED]
NORMALIZING THE LOADS
For comparisons to be made between the VAV systems with either series or parallel FPTUs, it was necessary that the system be subjected to the same cooling and heating load profiles. The space loads generated by the building model did not exactly match the capacities of the series or the parallel fan powered terminal units in either the 8 inch (200 mm) or 12 inch (300 mm) sizes. Each size/manufacturer had different primary air flow characteristics and as such had different rated cooling capacities. If a system designer were to select the proper FPTUs for a system operating in Houston, different units would likely have to be selected to operate for the same system operating in Phoenix or New York. To facilitate comparison of VAV systems in this study, the VAV system had to be able to "move" from one city to another.
Hourly cooling and heating loads for the three zone building were used to build load profiles for each zone at each city location. Hourly load profiles as a fraction of the peak load for a given hour and location were obtained by normalizing each zone load as shown in Equation 1,
Normalized [Load.sub.hr 10, New York] = [Peak [Load.sub.hr 10, New York]/Peak [Load.sub.New York]] (1)
Figure 4 shows a 24 hour normalized load profile for the South - West zone for each of the cities. Using the normalized profiles, a zone load could be scaled to the peak cooling capacity of the VAV terminal unit that was selected to handle a particular zone.
[FIGURE 4 OMITTED]
This technique allowed modeling of the operation of the facility at various geographic weather locations while maintaining the peak cooling loads within the capacity of the selected FPTU. This method also eliminated any bias in the simulation results if the VAV terminal units were either over or undersized when moved to different geographic locations.
THREE ZONE BUILDING MODEL
A three zone model was used for both the engineering model and experimental portion of this study. The load calculation process for each of the zones was as follows:
1. Add the hourly sensible and latent load from each zone and average the respective loads.
2. Repeat the first step for all hours during the year.
3. Divide all hourly values by the maximum value to normalize the load profile for the entire year (using Equation 1).
The combined loads for the three zone model were calculated only for the Houston location because of the high percentage of yearly operating hours in the cooling mode with high coincident latent load relative to the other geographical locations.
THREE ZONE TESTING POINTS
The Houston load data were reviewed and specific times during the year were selected as the operating points to be used with the experimental apparatus to verify the three zone model. The Houston data showed distinct variation in cooling and heating loads during the course of the year for the combined South/West and Core zone. Transitional periods where the interior space loads shift from predominantly cooling/heating to heating/cooling are also present in the Houston South/West zone data. This type of load profile causes a VAV system to switch from cooling to heating in a relatively short time span. This system behavior was important to include in the VAV system model and in the verification testing. As expected for an office building, the Houston Core zone was very consistent in load and was predominantly cooling year-round.
PRIMARY SYSTEM AND FPTU MODELS
The three zone system model was used to predict the operation of a VAV system and to develop a matrix of test points for the experimental setup. The experimentally measured values would then be compared to the predicted (model) values. This verification process ensured that the engineering system model could closely predict values obtained from a system operating under the same conditions. If the system model and the measured values did not agree, then adjustments could be made to the model to correct any calculation errors or improper assumptions.
Figure 5 shows a model flow diagram of a three zone single duct VAV system model using fan powered terminal units. Energy and mass balances were the primary engineering tool used to build the VAV system model. The system simulation procedure began with the calculation of the zone level conditions (Conditioned Space). Once the zone calculations were completed, the Return Air calculations were performed. The Mixed Air conditions after the introduction of Fresh Air were evaluated next and then the Preheat Coil conditions were estimated and the entering and leaving conditions for the Primary Fan were calculated. Following the Primary Fan, the entering and leaving Cooling Coil conditions were calculated. The properties of the air leaving the primary Cooling Coil were assumed to be the same as the primary air entering the VAV terminal unit. The engineering model was designed to mimic the behavior of a three zone VAV system. It had to predict the upstream static pressure, down stream static pressure, primary air flow, and induced air flow for a known space load at the FPTU as well as total VAV system response to these zone loads.
[FIGURE 5 OMITTED]
The VAV FPTU inlet valve position also had to be predicted by the model for a given set of duct conditions. It would not have been possible to verify the accuracy of the engineering model unless the upstream static pressure and the flow associated with the VAV valve position were accurately modeled. The details of the calculation procedures describing the VAV valve position control as well as all other primary VAV system calculations may be found in Davis et al. (2009).
THREE ZONE TEST STAND
A three zone system was designed and constructed to support an air distribution system consisting of three VAV zones. The model, as previously described, had been used to develop the testing points for use in the experimental test stand. A diagram of the system is shown in Figure 6. The diagram shows the test stand with a primary air plenum supplying air to three separately controllable duct systems which in turn, served three zones.
[FIGURE 6 OMITTED]
The sheet metal plenum supplying primary air to the three zones was connected to the primary air plenum of an 80-ton (281 kW) packaged rooftop air conditioner. The main fan for the packaged rooftop unit served as the primary supply air fan for the test stand.
Each of the three zones was connected to the primary air plenum with round sheet metal ducts. A butterfly damper was located at the connection point between the primary air plenum and the zone primary air duct. This damper was used to control the upstream static pressure supplied to each zone.
The supply duct consisted of rectangular sheet metal terminated at a supply register with an integrated opposed blade damper that was used to control the downstream static pressure. The speed of the terminal unit fans was controlled by adjusting a silicon controlled rectifier (SCR). Another actuator was used to adjust the SCR potentiometer to set the fan motor speed.
The entire setup was controlled by an off-the-shelf control system of a type typically used in building control applications. The operator of the test stand adjusted the actuator settings of each of the zones by issuing commands directly through the control system console. When a test was conducted, the actuators at each position in the test stand were set to control values pre-determined by the three zone model. Figure 7 shows the completed test stand.
[FIGURE 7 OMITTED]
THREE ZONE TEST MATRIX
A test matrix was developed that identified the critical test conditions for peak cooling and heating loads as well as moderate operating conditions expected in the spring and summer. The matrix supplied operational points for use in the experimental three zone system test stand. Normalized hourly load profiles were used to develop a test plan for the various FPTU sizes. The four daily profiles selected for testing were January 4, April 5, July 6, and September 28. These profiles were considered most likely to result in the operation of the VAV terminal units over their full range. The final normalized total hourly graph for these dates in Houston is shown in Figure 8.
[FIGURE 8 OMITTED]
After the operating load points were selected, the settings to be used for the test stand were determined for the FPTUs. The units were set up based on the peak cooling capacity of the terminal unit and the peak cooling load of the zone. Using the normalized loads that had been scaled to the capacity of the terminal unit, the test stand settings were established using the three zone series terminal unit model.
Table 1 shows the test stand control system and duct settings for each hour selected as a test point. The unit designation "S12C, S12B, and S8C" refer to a series FPTU from manufacturers B and C, and in 12 and 8 inch (200 and 300 mm) sizes. Note that the values shown in Table 1 are "predicted" values. That is, these are the values that resulted from the three zone engineering model evaluated at the specified zone conditions.
Table 1. FPTU Test Stand for a July 6 Operating Profile-Downstream Static held at 0.25 in. w.g. (62.2 Pa) and SCR held at 277 Vac Zone 1-S12C Zone 2-S12B Zone 3-S8C Hour Primary Primary Primary Primary Primary Primary Static in. Air Static, in. Air Static, Air w.g. (Pa) Damper, w.g. (Pa) Damper, in.w.g. Damper, Vde Vdc (Pa) Vdc 8 0.10 (24.9) 3.672 0.10 (24.9) 4.4 0.10 (24.9) 7.1 9 0.10 (24.9) 2.188 0.10 (24.9) 4.4 0.10 (24.9) 7.1 10 0.10 (24.9) 1.406 0.10 (24.9) 3.7 0.10 (24.9) 6.5 15 0.14 (34.9) 0.313 0.14 (34.9) 3.2 0.14 (34.9) 3.4 16 0.15 (37.4) 0.273 0.15 (37.4) 3.3 0.15 (37.4) 3.2 17 0.10 (24.9) 2.813 0.10 (24.9) 3.6 0.10 (24.9) 3.6
For example, the model predicts that for the load and system to be satisfied at 10am in the morning on July 6 in Zone 2 using FPTU S12B, primary static pressure must be 0.10 in.wg (24.9 Pa), the primary air damper control voltage must be 3.7 Vdc, the SCR control voltage is set at 277 Vac, and the downstream static has to be 0.25 in.wg (62.2 Pa).
The test stand was operated at the conditions outlined as shown in Table 1 to replicate the model parameters. The resulting discharge air temperature, FPTU power, and downstream static pressure data were recorded for comparison to the engineering model. This testing sequence was repeated for three other seasonal representative loads as shown in Figure 8.
THREE ZONE MODEL VERIFICATION AND RESULTS
The data gathered using the three zone test stand were used to perform the verification analysis of the three zone engineering model. Measured values of upstream static pressure, downstream static pressure, FPTU flow sensor pressure, primary air damper position, and SCR voltage were used in the three zone engineering model to generate a predicted supply air temperature ([T.sub.supply]). The predicted supply air temperatures were then compared to the actual measured supply temperatures from the test stand. Figures 9a and 9b show test data for parallel VAV FPTUs where data are shown from low to high airflow rates against predicted and measured [T.sub.supply]. This figure shows that the uncertainty in the predicted [T.sub.supply] is quite high for these units when they are operating at low airflow or primarily heating (low airflow) conditions. Throughout the "neutral" or cooling range of operation the test stand data agrees very with the engineering model predicted supply temperatures with uncertainty bands in the predicted temperature often overlapping the measured quantity. A detailed development of the uncertainty in the model predicted supply temperatures is given in Appendix A. The predicted supply temperature from the FPTU into a given zone is a function of the plenum supply temperature, zone room temperature, primary air flow into the FPTU, FPTU fan flow, and fan power used at the FPTU. Each of these have an associated uncertainty that show in the total propagated uncertainty for [T.sub.supply]. The test stand [T.sub.supply] measurement was an absolute measurement with an uncertainty of [+ or -] 0.7[degrees]F ([+ or -] 0.4[degrees]C).
[FIGURE 9 OMITTED]
SUMMARY AND CONCLUSIONS
Figure 10 shows the data grouped for the Parallel FPTU type and manufacturers that were used in this study. The largest spread in the model's [T.sub.supply] uncertainty occurred only at high supply air temperatures which are typically at the unit's lowest airflow rates.
[FIGURE 10 OMITTED]
This is an expected result as uncertainty in airflow measurements increases with decreasing airflow (uncertainty equations in Appendix A show a dominant airflow term in the denominator). As stated earlier, a typical VAV system only operates at design conditions a few hours out of the entire year. That type of operation is also the only time the system would be at maximum airflow. The majority of operation for these systems is somewhere in-between the maximum and minimum airflow for the FPTU.
The results shown in Figure 11 confirms the validity of the model. The percentage error was calculated between [T.sub.supply,measured] and [T.sub.supply,predicted] for the range of tested air flow rates. The average percentage error was +4.5%. That is, the model under predicts the [T.sub.supply] by about 4.5% compared to actual laboratory measurements.
[FIGURE 11 OMITTED]
The slight positive bias in the percentage error could be because of the constant value used for the specific heat of air in the model energy calculations (Davis et al 2009).
A Student-t test assuming equal variances was conducted on the [T.sub.supply] model and experimental data to verify the claim that the model is not statistically different from the experimental temperature values. The results of the Student-t test showed that at an alpha of 0.05, the Null Hypothesis was valid. That is, that there was no statistical difference between the two temperature data sets. Similar results were found for the Series units used in this study.
These results provided verification of the VAV FPTU model described in this paper and the basic three zone VAV model can now be expanded and more complex systems modeled with a high degree of confidence.
This work was a 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.
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.
Davis, M., Bryant, J., and O'Neal, D.L. 2009. Modeling the Performance of Single-Duct VAV Systems that use Fan Powered Terminal Units (RP-1292). ASHRAE Transactions 115(1).
Furr, J., O'Neal, D.L., Davis, M., Bryant, J., and Cramlet, A. 2008. Performance of VAV Parallel Fan-Powered Terminal Units: Experimental Results and Models (RP-1292). ASHRAE Transactions 115(1).
NREL. 1995. User's Manual for TMY2s (Typical Meteorological Years), NREL/SP-463-7668, and TMY2s, Typical Meteorological Years Derived from the 1961-1990 National Solar Radiation Data Base. Golden, CO: National Renewable Energy Laboratory.
For a FPTU in the fan "on" condition, Equation A1 gives an expression for the Supply Temperature ([T.sub.supply])
[T.sub.Supply] = [[[Q.sub.P][T.sub.P] + [Q.sub.F][T.sub.R] + [3.412[P.sub.Fan]/1.08]]/[[Q.sub.P] + [Q.sub.F]]] (A1)
Equation A2 is the uncertainty (see Kline et al. 1953) in the Supply Temperature ([T.sub.supply]) following from Equation A1 for an FPTU in the fan "on" condition:
u[T.sub.s] = [[[(([[T.sub.P]/[[Q.sub.P] + [Q.sub.F]]] - [[[Q.sub.P][T.sub.P] + [Q.sub.F][T.sub.R] + 3.16[P.sub.Fan]]/[([Q.sub.P] + [Q.sub.F]).sup.2]])u[Q.sub.P]).sup.2] + [([[Q.sup.P]/[[Q.sub.P] + [Q.sub.F]]]u[T.sub.P]).sup.2] + [(([[T.sup.R]/[[Q.sub.P] + [Q.sup.F]]] - [[[Q.sub.P][T.sup.P] + [Q.sub.F][T.sup.R] + 3.16[P.sub.Fan]]/[([Q.sub.P] + [Q.sub.F]).sup.2]])u[Q.sup.F]).sup.2] + [([[Q.sup.F]/[[Q.sup.P] + [Q.sup.F]]]u[T.sup.R]).sup.2] + ([3.16/[[Q.sup.P] + [Q.sup.F]]]u[P.sub.Fan])].sup.[1/2]] (A2)
u[T.sub.s] = uncertainty in estimated supply temperature
[T.sub.p] = measured plenum supply temperature (also referred to as Tsupply)
u[T.sub.p] = uncertainty in plenum supply temperature (assumed to be [+ or -]0.7F)
[T.sub.R] = measured room temperature
u[T.sub.R] = uncertainty in room temperature (assumed to be [+ or -]0.7F)
[Q.sub.P] = measured Primary air flow rate into the FPTU
[Q.sub.F] = measured Fan air flow rate
[P.sub.Fan] = power used by the FPTU fan motor
u[Q.sub.P] = uncertainty in primary air flow, see equation (A4)
u[Q.sub.F] = uncertainty in FPTU fan air flow
Total propagated uncertainty would then be expressed as [T.sub.s] [+ or -] u[T.sub.s].
The expression for when the FPTU is in the fan "off condition is given as
[T.sub.s] = [T.sub.P] + [3.412[P.sub.Htr]/1.08[Q.sub.S]] (A3)
Propagated uncertainty in [T.sub.supply] for this case is given by
u[T.sub.S] = [[(u[T.sub.P]).sup.2] + [(3.16u[P.sub.Htr]/[Q.sub.S]).sup.2] + [(3.16[P.sub.Htr]u[Q.sub.S]/[Q.sub.S].sup.2]].sup.[1/2]] (A4)
A previous study generated correlating equations for use with the parallel fan powered terminal units used in this study (Furr 2007). Uncertainty for the flow in these units was estimated using these correlations and, depending on the unit, the uncertainty equation is as follows.
u[Q.sup.P] = [[((C1(1 + C2 x s + C3 x [S.sup.2])[([P.sub.up] - [P.sub.dn]).sup.[1/2]])uDmpr).sup.2] + [((0.5C1([1 + C2 X S + C3 X [S.sup.2]]/[([P.sup.up] - [P.sub.dn]).sup.[1/2]]))u[P.sup.up]).sup.2] + [((-0.5 C1([1 + C2 X S + C3 X [S.sup.2]]/[([P.sub.up] - [P.sub.dn]).sup.[1/2]]))u[P.sup.up]).sup.2]] (A5)
Dmpr is the damper setting (in degrees), uDmpr is the uncertainty in the damper setting (assumed as [+ or -]5 degrees), and u[P.sub.up] and u[P.sub.dwn] are the uncertainty in the upstream and downstream static pressures. The coefficients C1, C2, and C3 depend on which box is being used. Those coefficients are given in Table A1.
John A. Bryant, PhD, PE
APPENDIX A REFERENCES
Kline, S. J., and F A. McClintock. 1953. Describing Uncertainties in Single-Sample Experiments. Mech. Eng., p. 3.
Furr, J., D.L. O'Neal, M. Davis, J. Bryant, and A. Cramlet. 2007. Performance of VAV Parallel Fan-Powered Terminal Units: Experimental Results and Models (RP-1292). ASHRAE Transactions.
Table A1. Coefficients for Parallel FPTUs from Flow Correlations (Furr 2007) Box C1 C2 C3 P8A 1,362.9 -2.020E-02 9.870E-05 P8B 1,935.0 -2.480E-02 1.910E-04 P8C 1,593.8 -2.730E-02 1.910E-04 P12A 7,425.1 -3.070E-02 2.050E-04 P12B 5,781.2 -2.770E-02 2.040E-04
John A. Bryant, PhD, PE
Dennis L. O'Neal, PhD, PE
Michael A. Davis
Associate Member ASHRAE
This paper is based on findings resulting from ASHRAE Research Project RP-1292.
John A. Bryant is an associate professor in the Mechanical Engineering Program and Michael A. Davis is a research engineer at the Texas A&M University at Qatar. Dennis L. O'Neal is a professor and head of the Mechanical Engin6eering Department and Andrew Cramlet completed graduate studies in the Mechanical Engineering Department at Texas A&M University in College Station, TX.
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|Title Annotation:||variable air volume|
|Author:||Bryant, John A.; O'Neal, Dennis L.; Davis, Michael A.; Cramlet, Andrew|
|Date:||Jan 1, 2009|
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