# Virtual flow meter to estimate the water flow rates in chillers.

INTRODUCTIONVirtual sensors are becoming more and more popular in the heating, ventilation and air-conditioning (HVAC) industry to provide information, in the absence of sensors, for detailed monitoring, and intelligent building controls for the existing building commissioning or ongoing commissioning. Chilled and condenser water flow rates are important parameters in the assessment of energy performance of HVAC systems and equipment, and in the detection of faults in chillers and condenser water loops (Comstock et al. 1999; Jia et al. 2003; Reddy 2006; Zhou et al. 2009; Zhao et al. 2012). Most often, water flow meters are not installed in central cooling plants because of high installation, maintenance and recalibration costs. Flow meters typically require a long, straight pipe free of flow disturbances before and after the meter to provide accurate results, which is not always available in central plants of commercial and institutional buildings (Zhao et al. 2012).

An alternative solution is the use of a portable ultrasonic flow meter that provides nonintrusive short-term measurements of the chilled and condenser water mass flow rate. This approach is not suited for long-term measurements for ongoing commissioning, especially in the case of variable flow rates. There is a need for a low-cost alternative method to calculate the mass flow rate in the chilled and condenser fluid loops, in the absence of water flow meters.

The term "virtual meter" or "virtual sensor" was recently used in publications to identify a mathematical model used for the calculation of missing measurements. Song et al. (2012) and Wang et al. (2010) developed models to estimate the water mass flow rate leaving a pump using other measurements available at the pump such as the pump speed, the motor power and pump characteristic data. One common problem with both models is the sensitivity of the measuring equipment.

Zhao et al. (2012) used information from the chiller to predict, under different types of chiller faults and fault severity, the refrigerant mass flow rate of a single-stage laboratory centrifugal chiller, and the chilled and condenser water mass flow rates in the laboratory setting and field monitoring of a single-stage centrifugal chiller.

The chilled and condenser water mass flow rates can also be estimated by measuring the pressure drop across the evaporator and condenser and correlating these measurements with the manufacturer's information for the flow rate vs. pressure drop (Taylor 2004). Trane (2013) has used this methodology in their CenTraVac chillers to provide an estimated chilled and condenser mass flow rate.

PROPOSED VIRTUAL WATER FLOW METERS (VFMS)

This paper presents two VFMs, models A and B, to estimate the chilled and condenser water mass flow rates from available measured data from a BAS. Five scenarios are considered with a different number of sensors: the first scenario uses ten sensors, while the last scenario uses six sensors. When the amount of sensors is reduced, some manufacturer data is included to fill the gaps left by the missing sensors.

VFM models A and B estimate under steady-state conditions the chilled and condenser water mass flow rates of chillers with reciprocating and centrifugal compressors. When the number of sensors is reduced to the point where there is not sufficient information available to use VFM model A, the VFM model B is used. Both VFM models use the energy balance on the evaporator and condenser, respectively, in determining the chilled and condenser mass flow rates. The main difference is the method used to estimate the refrigerant mass flow rate. VFM models A and B use the energy balance on the compressor when all or most information at that level is available; when additional information is needed, data for the missing sensors is calculated by using the compressor identification parameters technique the ASHRAE Primary HVAC Toolkit I (Bourdouxhe et al. 1994). Both VFMs use a steady-state component thermodynamic analysis of a vapour compression chiller which comprises a compressor, a condenser loop, an expansion device and an evaporator loop (Figure 1). The ideal VFM model A (scenario number 1) requires ten sensors, which are not always available in existing buildings or connected to a BAS, since they not typically required in the commissioning process, it is difficult to justify to the building owner. The challenge is to obtain good estimates of the chilled and condenser water flow rates when the number of sensors is reduced.

Both models were programmed in Matlab to allow the simple execution of the models. Matlab was chosen as the programming language because of its capability to handle a large amount of data efficiently, the available toolkits for data analysis, and the ease of coupling with REFPROP (Lemmon et al. 2013), developed by the National Institute of Standard and Technology (NIST), by a dynamic link library (DLL), to calculate the refrigerant thermodynamic properties of refrigerants commonly used in refrigeration systems.

The uncertainties associated with calculation of the thermodynamic properties of a refrigerant are taken into consideration for the uncertainty analysis of the VFM models.

VFM MODEL A

The mathematical model developed by Zhao et al. (2012), which will be denoted as VFM model A, estimates the chilled and condenser mass flow rates using measurements from the sensors embedded inside a chiller, which are connected to the BAS. The only modification in this paper in the VFM model A, compared to the original model developed by Zhao et al. (2012), is the use of measured actual power input to the compressor ([W.sub.ac]) to evaluate the refrigerant mass flow rate (Equation 1), instead of the theoretical power input to the compressor ([W.sub.th]). The refrigerant mass flow rate of the vapour compression cycle is calculated by using the energy balance on the compressor assuming an adiabatic compression where no heat is lost to the exterior. The chilled and condenser water mass flow rates are calculated by applying an energy balance on the evaporator (Equation 2) and condenser (Equation 3).

[m.sub.r] = [W.sub.ac]/[[h.sub.dis] - [h.sub.suc]] (1)

[m.sub.chw] = [m.sub.r]([h.sub.suc] - [h.sub.ll])/[c.sub.p]([T.sub.chwr] - [T.sub.chws]) (2)

[m.sub.cd] = [m.sub.r]([h.sub.dis] - [h.sub.ll])/[c.sub.p]([T.sub.cdwr] - [T.sub.cdws]) (3)

where [h.sub.suc] is the suction enthalpy that is calculated using the pressure in the evaporator and the suction temperature, [h.sub.dis] is the discharge enthalpy that is calculated from the condenser pressure and the discharge temperature, and [W.sub.ac] is the actual compressor power input, [h.sub.ll] is the liquid line enthalpy that is calculated from the pressure in the condenser and the liquid line temperature. VFM model A can be used for scenarios 1, 2, and 3 based on available data; however, it cannot be used for scenarios 4 and 5 because information of the discharge temperature is not available. In the absence of a measurement or manufacturer data to determine the discharge temperature,

VFM model B can be used to estimate the chilled and condenser water flow rates.

VFM model B uses the subroutines from ASHRAE Primary HVAC Toolkit I (Bourdouxheetal. 1994) to obtain the compressor identification parameters, which are used to estimate the refrigerant mass flow rate for the compressor. The flowchart of the VFM model B, is shown in Figure 2. The user selects the refrigerant and compressor type, and attaches two data files: (1) one file with the scenario code and measurements from the chiller over the period of investigation, and (2) another file, a data file of manufacturer data.

VFM model B first calculates the steady-state compressor identification parameters for either a reciprocating or centrifugal compressor using the subroutines PISCOMP1 and CENTHID, respectively, from the ASHRAE Primary HVAC Toolkit I (Bourdouxhe et al. 1994). Manufacturer data files (MD-1) cover the range of operation conditions of the compressor. For each compressor (reciprocating and centrifugal) the subroutines (PISCOMP1 and CENTHID) were modified and written into Matlab to identify the compressor parameters used to estimate the refrigerant mass flow rate of the vapour compression cycle. The common parameters for all three subroutines are: the electromechanical losses ([W.sub.lo]) and the loss factor ([alpha]) which allow to estimate the goodness of the fit of the parameters to the manufacturer data. The compressor parameters are then used to calculate the refrigerant mass flow rate.

Reciprocating. The refrigerant mass flow rate for the reciprocating compressor is calculated by Equation 4 which uses the identified compressor parameters the clearance factor of the compressor ([C.sub.f]) and the geometric displacement of the compressor ([V.sub.s]). The specific volume after heating up ([v.sub.1']) is calculated using the suction temperature and the pressure in the evaporator as shown in Equation 5.

[m.sub.r] = [1 + [C.sub.f] + [C.sub.f][([P.sub.cd]/[P.sub.ev]).sup.1/[gamma]]][V.sub.s]/[v.sub.1'] (4)

[v.sub.1'] = [zeta]r[T.sub.suc]/[P.sub.ev] (5)

Centrifugal. The refrigerant mass flow rate for the single stage centrifugal compressor is calculated by Equation 6, where the identified compressor parameters: the impeller exhaust area (A), the peripheral speed of the impeller (U), and the angle between the direction of the vanes at the impeller exhaust and the plane tangent to the impeller circumference ([beta]) are used to calculate the refrigerant volume flow rate at the impeller exhaust (V) by Equation 7 and the impeller pressure ratio ([[pi].sub.i]) by Equation 8.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

{[[gamma]/[[gamma] - 1]]][zeta]r[T.sub.suc][[[([P.sub.ev]/[P.sub.cd]).sup.[[gamma] - 1]/[gamma]] -1] - [U.sup.2]} (8)

VFM model B calculates the mass flow rates as in VFM model A (Equation 2), but for the condenser water mass flow rate, Equation 9 is used instead of Equation 3 in the absence of measured discharge temperature.

[m.sub.cd] = [[m.sub.r]([h.sub.suc] - [h.sub.ll]) + [W.sub.ac]]/[c.sub.p]([T.sub.cdwr] - [T.sub.cdws]) (9)

DESCRIPTION OF SCENARIOS OF INPUT DATA

The main challenge in the implementation of VFMs in existing buildings is the availability of required sensors. Five different scenarios of measured data are presented in this section to represent the best to worst case of available measurements from existing buildings in operation. Scenarios 1, 2, and 3 are used to evaluate VFM model A, while scenarios 4 and 5 are used to evaluate VFM model B (Table 1).

MD-1 is the manufacturer data that is used to estimate the refrigerant mass flow rate of the vapour compression cycle for scenarios 4 and 5 using the Primary HVAC Toolkit I (Bourdouxhe et al. 1994). MD- 2 is the manufacturer data used to estimate the discharge temperature ([T.sub.dis]), which is the temperature at the exit of the compressor. The saturation temperature in the evaporator ([T.sub.ev]) and the saturation temperature in the condenser ([T.sub.cd]) are directly linked to the saturation pressure in the evaporator ([P.sub.ev]) and condenser ([P.sub.cd]). The methodology assumes that there is minimal pressure loss in the system from the condenser to the expansion valve and from the evaporator to before the compressor. The suction temperature ([T.sub.suc]) is assumed to operate close to the evaporator pressure and is measured just before the compressor after heating up by the degree of superheating ([DELTA][T.sub.supheat]). If the pressure can also be determined just before the compressor this value would be used instead to determine the suction enthalpy ([h.sub.suc]). The liquid-line temperature is measured just before the thermal expansion valve (TEV), is assumed to operate close to the condenser pressure, and is lower than the saturation temperature in the condenser by the degree of subcooling ([DELTA][T.sub.subcool]). If the pressure can be determined just before the TEV, this value would be used instead of the condensing pressure to determine the liquid line enthalpy ([h.sub.ll]). The supply and return chilled and condenser water temperatures ([T.sub.chws], [T.sub.chwr], [T.sub.cdws], and [T.sub.cdwr]) are measured at the outlet and inlet of the evaporator and condenser respectively. The compressor's actual power input ([W.sub.ac]) is measured either directly from the chillers' onboard measurements or by a power meter installed on the electric panel.

The five scenarios are presented as follows:

1. Scenario 1 uses a complete data set with ten measured inputs.

2. Scenario 2 uses nine measured inputs, where the discharge temperature (Tdis) is estimated from manufacturer data as follows:

[T.sub.dis] = [T.sub.suc] [([P.sub.cd]/[P.sub.ev]).sup.[n-1]/n] (10)

n/[n - 1] = [k/[k - 1]][[eta].sub.p] (11)

In some cases, short-term measurements of the wall pipe temperature can be used. If it is not possible to provide an estimate for the discharge temperature, VFM model A cannot be used to estimate the chilled and condenser water mass flow rates. Hence, VFM model B is used with data available from scenario 4 or 5.

3. Scenario 3 uses seven measured inputs and three inputs that need to be estimated (Table 1). This is a common scenario for information available from a BAS system. The estimated inputs are the suction temperature ([T.sub.suc]), discharge temperature ([T.sub.dis]), and the liquid line temperature ([T.sub.ll]). The discharge temperature can be estimatedby the methods presented in scenario 2. To estimate the suction temperature ([T.sub.suc]) a temperature sensor can be placed on the suction line of the compressor, on the pipe wall underneath the insulation layer. Then the amount of superheating ([DELTA][T.sub.supheat]) can be determined by Equation 12. To estimate the liquid line temperature, ([T.sub.ll]) a temperature senor can be placed at the exit of the condenser of the chiller to measure the mean temperature at that loca tion for a certain period. Then the amount of subcooling ([DELTA][T.sub.subcool]) can be determined by Equation 13.

[DELTA][T.sub.superheat] = [T.sub.suc] - [T.sub.ev] (12)

[DELTA][T.sub.subcool] = [T.sub.ll] - [T.sub.cd] (13)

The installation of new sensors can be used to determine the superheating and subcooling of the system by two methods: 1) installing sensor wells, an intrusive method that would provide the most accurate measurements, but it is not an acceptable solution because of the practical problems it could create; 2) installing pipe surface temperature sensors by either using thermally conductive epoxy to clean copper or if possible other pipe surface sensors like thermal ribbons. Some manufacturers provide data for the superheating and subcooling over the range of loading of the chiller which would allow for the easy estimation of the suction and liquid line temperatures. In the absence of information on the superheating and subcooling, the suction and liquid line temperatures can also be estimated by using manufacturer data for the amount of superheating and subcooling from similar chiller systems by the experience of refrigerating professionals. Also previous case studies that contain similar systems could be used to provide estimates of the amount of superheating and subcooling.

4. Scenario 4 uses eight measured inputs. The discharge temperature and the power input into the compressor are not required as inputs into the model.

5. Scenario 5 uses six measured data that represent the minimum number of sensors used in combination with manufacturer data to obtain the chilled and condenser water mass flow rates.

CASE STUDY

The two VFM models A and B were used with measurements collected by CANMET-Varennes Energy Technology Center of an ice arena located in Montreal, Quebec for ASHRAE Research Project RP-1289 (Ouzzane et al. 2006, Teyssedou et al. 2009). This case study was selected because the number of sensors installed on the system allows for the evaluation of VFM models for scenarios 2 to 5, and compare the estimates with measurements on a reciprocating compressor with air-cooled condenser.

Description of Monitoring System

The Camillien-Houde arena was monitored by CANMET-Varennes Energy Technology Center (Ouzzane et al. 2006) over a period of time using sensors and data loggers to collect information about the operating conditions of the refrigeration system to determine the cooling load of the arena. Two different types of measurements were used, long and short term. Long-term measurements were collected over several days of operations by permanently installed sensors (Table 2). These measurements were collected on a one minute basis and transferred to a computer though an internet connection. The short-term measurements were collected using portable instruments and were performed outside of the regular hours of use of the ice rink and with all five compressors in operation (Table 3). The measurements used in this case study extend from December 2005 to May 2006 and October to November 2006 where a period of two days were monitored for each month.

A portable ultrasonic flow meter was used just after the expansion valve to measure the refrigerant volumetric mass flow rate. The refrigerant mass flow rate of 0.335 kg/s (44.24 lb/min) was derived from the measured refrigerant volumetric flow rate of 0.287 L/s (4.55 gpm) (Ouzzane et al. 2006).

VFM MODEL DEVELOPMENT FOR THE CAMILLIEN-HOUDE ARENA

From the information available for the Camillien-Houde arena both VFM models A and B can be used to estimate the mass flow rate of the chilled water loop. In this section, the assumptions used in each VFM model for each chosen scenario are outlined to understand the method of the VFM models. The first step for both models is to obtain the refrigerant mass flow rate to then be used to obtain the chilled water mass flow rate. VFM model A and B calculate the refrigerant mass flow using different techniques while they calculate the chilled water mass flow rate using the same methodology. For this, the methods used to calculate the refrigerant mass flow rate are demonstrated for both models while the method to calculate the chilled water mass flow rate are shown together.

In the absence of a temperature sensor to measure the discharge temperature ([T.sub.dis]) VFM model A can be used with scenarios 2 and 3. For this case study the discharge temperature can be estimated by employing an empirical equation provided by the compressor's manufacturer (Carrier Corporation 2001) which relates the discharge temperature to the suction temperature ([T.sub.suc]) by a constant C shown in Equation 14.

[T.sub.dis] = C x [T.sub.suc] (14)

The constant C is derived from laboratory experiments that relate the condenser pressure to the evaporator pressure by the polytropic compression exponent (n) shown in Equation 15.

C = [([P.sub.cd]/[P.sub.ev]).sup.[n-1]/n] (15)

For a compressor operating with refrigerant R-22 without water cooled heads the polytropic compression exponent (n) is equal to 1.23, leading to a constant C =1.40 (Carrier Corporation 2001). The discharge enthalpy ([h.sub.dis]) can be evaluated by using the discharge temperature and the condenser pressure.

Scenario 3 requires that the suction ([T.sub.suc]) and liquid line temperatures ([T.sub.ll]) to be estimated by using a constant degree of superheating ([DELTA][T.sub.Supheat]) and subcooling ([DELTA][T.sub.subcool]). Because the suction and liquid line temperatures are measured during the operation, the task of estimating these values is simplified. The evaporator operates at a pressure of 263.4 kPa (38.2 psia), which results in a refrigerant saturation temperature of 18.48[degrees]C (-1.16[degrees]F). The mean measurement for the suction temperature is -13.22[degrees]C (8.2[degrees]F) which results in a superheating ([DELTA][T.sub.supheat]) of 5.26[degrees]C (9.47[degrees]F). The condenser operates at 1550 kPa (225 psia) which results in a refrigerant saturation temperature of 40.43[degrees]C (104.78[degrees]F). The mean liquid line temperature is 30.10[degrees]C (86.18[degrees]F) which results in a subcooling ([DELTA][T.sub.subcool]) of 10.33[degrees]C (18.6[degrees]F). Experts from CANMET-Varennes recommended a superheating and subcooling of 6[degrees]C (10.8[degrees]F) and 12.5[degrees]C (22.5[degrees]F) respectively over the range of operation the compressors (Teyssedou 2007).

VFM model B can be evaluated using scenario 4s and 5 for this case study. The inputs required for each scenario are shown in Table 1. The refrigerant mass flow rate for VFM model B is determined by using the subroutine PISCOMP1 of the ASHRAE Primary HVAC Toolkit I (Bourdouxhe et al. 1994). An input file (MD-1) composed of manufacturer data is required to identify the parameters of the reciprocating compressor. The input file was compiled from manufacturer data from Carwin (Carlyle Compressor Company 2007) the manufacturer compressor selection software from Carrier. Because PISCOMP1 uses an iterative process the data file needs to cover a range of evaporating and condensing temperatures to provide accurate parameters. The data file was created to cover the range of operation of the compressors in the Camillien-Houde arena. The saturation suction temperature (SST) was ranged from -20[degrees]C (-4[degrees]F) to -6[degrees]C (21.2[degrees]F) by 2[degrees]C (3.6[degrees]F) increments and ranging the saturation discharge temperature (SDT) from 35[degrees]C (95[degrees]F) to 45[degrees]C (113[degrees]F) by 5[degrees]C (9[degrees]F) for each evaporator temperature. The refrigerant capacity (Qev) and the power input ([W.sub.ac]) to the compressor for each working point were determined by Carwin, the compressor software.

ESTIMATES OF REFRIGERANT MASS FLOW RATES

Table 4 shows for comparison purposes the average refrigerant mass flow rates calculated over a two-day period of each month by the VFM models for the four scenarios (numbers 2 to 5), the calculated refrigerant mass flow rate using Carwin (Carlyle Compressor Company 2007), the compressor selection software, and the measured value by Ouzzane et al. (2006). Table 4 also contains the uncertainty propagation due to measurements. While sensors collect data every minute, the refrigerant mass flow rate was calculated as the average over a 15-minute interval.

Under the scenarios 2 and 3, which use the VFM model A, the refrigerant mass flow shows a slight variation from month to month, which could be because of the small variation of the power input into the compressor and the uncertainty in the method used to determine the measured power input to the compressor ([W.sub.ac]). Scenarios 4 and 5 which use the VFM model B give constant values for the refrigerant mass flow rate because they use the average compressor identification parameters generated from the ASHRAE Primary HVAC Toolkit I (Bourdouxhe et al. 1994). The uncertainties due to measurements are not calculated for scenarios 4 and 5 because it is difficult to estimate the uncertainties due to measurements for the subroutine PISCOMP1 from ASHRAE Primary HVAC Toolkit I (Bour douxhe et al. 1994). The compressors are assumed to operate at a constant compression ratio of 5.962 which causes the volumetric effectiveness ([[epsilon].sub.vol]) of the compressor to be constant as well. The only input which changes in scenario number 4 is the measured suction temperature. The average values for the refrigerant mass flow rate for all scenarios agree well with the results from the manufacturer and also the measured value from Ouzzane et al. (2006) as the largest percent difference is less than 14%, while scenarios 4 and 5 have the lowest percent difference with less than 4%. The refrigerant mass flow only changes slightly between each scenario with the largest percent difference between the two VFM models A and B being 4%.

RESULTS OF BOTH VFM MODELS FOR THE CHILLED WATER MASS FLOW RATE

The chilled water mass flow rate was estimated on a 15-minute interval using the information from sensors and available data from chiller #1 for the chilled water loop of the Camillien-Houde arena. There are three refrigerant loops which pass through the evaporator of chiller #1, which are assumed to have equal refrigerant capacity. Therefore, the chilled water mass flow rate for both VFM models A and B was calculated using Equation 16.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

where N is the number of refrigerant fluid loops which pass through the evaporator, [m.sub.r] is the refrigerant mass flow rate of each loop, [h.sub.suc] is the suction enthalpy, [h.sub.ll] the liquid line enthalpy, [C.sub.p] is the specific heat capacity of the chilled water, [T.sub.chwr] is the chilled water return temperature after the pump, [T.sub.chws] is the chilled water supply temperature. Table 5 contains the average estimates of the chilled mass flow rate for each two days under investigation for each month and the uncertainty propagation due to measurements.

The estimation of the average chilled water mass flow rate varies from 55.6 kg/s (7355 lb/min) (scenario 4) to 58.5 kg/s (7738 lb/min) (scenario 3) compared with 63.1 kg/s (8347 lb/ min) measured by Ouzzane et al. (2006), a difference of 11.9% to 7.29%, respectively, for the year under investigation. The large difference between the mean monthly values can be because of the small [DELTA][T.sub.chw] between the chilled water return and supply temperature of the evaporator of chiller #1. Because the average [DELTA][T.sub.chw] for each month is small and varies from 0.75[degrees]C (1.35[degrees]F) to 1.18[degrees]C (2.12[degrees]F) the chilled water mass flow rate is very sensitive to the small changers in [DELTA][T.sub.chw]. This small change could be attributed to the uncertainty of the temperature measurements. For this case study, scenarios 4 and 5 predict the yearly average chilled water mass flow rates within 5% of scenarios 2 and 3, showing that for this case study the accuracy of the model was not greatly affected by the reduction in available sensors.

CONCLUSION

This paper has presented the two VFMs used to estimate the chilled and condenser water mass flow rates of chillers, which were applied under different scenarios of available measured data commonly found in a BAS. The two VFM models provide a low-cost, nonintrusive method for the ongoing commissioning of existing central cooling plants. The VFM models provided good estimates for a case study when compared with measurements. This case study also shows good estimates between the VFM model B with six sensors, combined with manufacturer data, with that of VFM model A using nine sensors showing the accuracy of the model is not greatly affected by the reduction in available sensors.

Future work will examine the models performance using data that covers the complete cooling season on a time scale suited for ongoing commissioning and will address a two-stage centrifugal chiller with measurements covering fifteen-minute intervals over the entire cooling season.

NOMENCLATURE [alpha] = loss factor A = impeller exhaust area [beta] = angle between the direction of the vanes at the impeller exhaust and the plane tangent to the impeller circumference [C.sub.f] = clearance factor of the compressor [C.sub.p] = specific heat of water a constant pressure [gamma] = mean isentropic coefficient [h.sub.dis] = refrigerant discharge enthalpy [h.sub.ll] = refrigerant liquid line enthalpy [h.sub.suc] = refrigerant suction enthalpy k = adiabatic compression exponent [m.sub.chw] = chilled water mass flow rate [m.sub.cd] = condenser mass flow rate [m.sub.r] = refrigerant mass flow rate n = polytropic exponent [[eta].sub.p] = isentropic efficiency of compressor [P.sub.cd] = saturation condenser pressure [P.sub.ev] = saturation evaporator pressure r = refrigerant gas constant [T.sub.dis] = refrigerant temperature at compressor outlet [T.sub.cdwr] = condenser water return temperature [T.sub.cdws] = condenser water supply temperature [T.sub.chwr] = evaporator water return temperature [T.sub.chws] = evaporator water supply temperature [T.sub.ll] = liquid line refrigerant temperature [T.sub.suc] = refrigerant temperature at compressor inlet U = peripheral speed of the impeller [v.sub.1] = actual compressor power input [V.sub.s] = geometric displacement of the compressor [W.sub.ac] = actual compressor power input [W.sub.lo] = actual compressor power input [zeta] = mean compressibility factor

ACKNOWLEDGMENT

The authors acknowledge the financial support from NSERC Smart Net-Zero Energy Building Strategic Research Network and the Faculty of Engineering and Computer Science of Concordia University.

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Eric McDonald

Student Member ASHRAE

Radu Zmeureanu, PEng, PhD

Member ASHRAE

Eric McDonald is a graduate student in the Department of Building Engineering and Radu Zmeureanu is a professor in the Department of Building, Civil, and Environmental Engineering, Concordia University, Montreal, Quebec, Canada.

Table 1. Scenarios of Available Measured Data Description of Symbol Scenario Points 1 2 3 4 5 Chilled water [T.sub.chwr], M M M M M supply and [T.sub.chws] return temperatures Condenser [T.sub.cdwr], M M M M M water supply [T.sub.cdws] and return temperatures Pressure or [T.sub.ev], M M M M M temperature in [P.sub.ev] evaporator Pressure or [T.sub.cd], M M M M M temperature in [P.sub.cd] condenser Suction [T.sub.suc] M M E M E temperature Discharge [T.sub.dis] M MD-2 MD-2 -- -- temperature Liquid line [T.sub.11] M M E M E temperature Power input [W.sub.ac] M M M -- -- into the compressor Manufacturer -- -- -- -- MD-1 MD-1 data Table 2. Description of Long-Term Measurements Used in This Study (Ouzzane et al. 2006) Measurement Symbol Instrument Suction temperature [T.sub.suc] Thermocouple Liquid line [T.sub.11] Thermocouple temperature chilled water inlet [T.sub.chwr] Thermocouple temperature Chilled water outlet [T.sub.chwr] Thermocouple temperature Electric power demand [W.sub.ac] Power demand transmitter Measurement Accuracy Sensitivity [degrees]C [degrees]C ([degrees]F) ([degrees]F) Suction temperature [+ or -] 0.1 (0.18) [+ or -] 0.01 (0.18) Liquid line [+ or -] 0.1 (0.18) [+ or -] 0.01 (0.18) temperature chilled water inlet [+ or -] 0.1 (0.18) [+ or -] 0.01 (0.18) temperature Chilled water outlet [+ or -] 0.1 (0.18) [+ or -] 0.01 (0.18) temperature Electric power demand [+ or -] 5% -- Table 3. Description of Short-Term Measurements Used in This Study (Ouzzane et al. 2006) Measurement Symbol Instrument Evaporator and [P.sub.ev], Manometer condenser pressure [P.sub.ed] Refrigerant mass Portable flow rate ultrasonic flow meter Chilled water mass Portable flow rate ultrasonic flow meter Measurement Accuracy Sensitivity Evaporator and -- -- condenser pressure Refrigerant mass [+ or -] 0.5%-2% [+ or -] 0.1% flow rate at 40[degrees] (104[degrees]F) Chilled water mass [+ or -] 0.5%-2% [+ or -] 0.1% flow rate at 40[degrees] (104[degrees]F) Table 4. Comparison of Daily Average Refrigerant Mass Flow Rate Daily Average Refrigerant Mass Date Flow Rate, kg/s (lb/min) Scenario 2 Scenario 3 December 06-07, 2005 0.368 (48.68) 0.380 (50.26) February 9-10, 2006 0.377 (49.87) 0.377 (49.87) March 14-15, 2006 0.357 (47.22) 0.358 (47.36) April 14-15,2006 0.334 (41.18) 0.333 (44.05) May 13-14, 2006 0.328 (43.39) 0.330 (43.65) October 17-19, 2006 0.375 (49.60) 0.376 (49.74) November 10-11, 2006 0.379 (50.13) 0.380 (50.26) Average of estimates 0.360 [+ or -] 0.017 0.362 [+ or -] 0.017 (47.62 [+ or -] 2.25) (47.88 [+ or -] 2.25) Calculated by Manufacturer Software Carlyle Compressor 0.343 (45.37) Company (2007) Measured Ouzzane et al. (2006) 0.335 [+ or -] 0.00681 (44.31 [+ or -] 0.90) Date Daily Average Refrigerant Mass Flow Rate, kg/s (lb/min) Scenario 4 Scenario 5 December 06-07, 2005 0.348 (46.03) 0.347 (45.90) February 9-10, 2006 0.346 (45.77) 0.347 (45.90) March 14-15, 2006 0.347 (45.90) 0.347 (45.90) April 14-15,2006 0.347 (45.90) 0.347 (45.90) May 13-14, 2006 0.347 (45.90) 0.347 (45.90) October 17-19, 2006 0.347 (45.90) 0.347 (45.90) November 10-11, 2006 0.347 (45.90) 0.347 (45.90) Average of estimates 0.347 (45.90) 0.347 (45.90) Carlyle Compressor Company (2007) Ouzzane et al. (2006) Table 5. Comparison of Daily Mean Values of the Chilled Water Mass Flow Rate Date Average Refrigerant Mass Flow Rate kg/s (lb/min) 2 3 December 06-07 2005, 59.1 (7817) 63.1 (8347) February 9-10 2006, 53.3 (7050) 53.8 (7116) March 14-15 2006, 50.6 (6693) 51.2 (6773) April 14-15 2006, 62.6 (8280) 63.2 (8360) May 13-14 2006, 68.9 (9114) 70.3 (9299) October 17-19 2006, 54.4 (7196) 55.3 (7315) November 10-11 2006, 51.9 (6865) 52.7 (6971) Average of estimates, 57.3 [+ or -] 17.33 58.5 [+ or -] 17.27 (7579 [+ or -] 2292) (7738 [+ or -] 2284) Measured Ouzzane et al. 2006 63.1 [+ or -] 5.24 (8347 [+ or -] 693) Date Average Refrigerant Mass Flow Rate kg/s (lb/min) 4 5 December 06-07 2005, 55.1 (7288) 57.5 (7506) February 9-10 2006, 48.8 (6455) 49.4 (6534) March 14-15 2006, 49.2 (6508) 49.7 (6574) April 14-15 2006, 66.8 (8836) 67.5 (8929) May 13-14 2006, 73.5 (9722) 74.3 (9828) October 17-19 2006, 49.8 (6587) 50.4 (6667) November 10-11 2006, 48.5 (6415) 49.1 (6495) Average of estimates, 55.6 [+ or -] 16.84 56.8 [+ or -] 16.85 (7355 [+ or -] 2228) (7513 [+ or -] 2229) Ouzzane et al. 2006 63.1 [+ or -] 5.24 (8347 [+ or -] 693)

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Author: | McDonald, Eric; Zmeureanu, Radu |
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Publication: | ASHRAE Transactions |

Article Type: | Report |

Date: | Jul 1, 2014 |

Words: | 5978 |

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