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Chiller Models

Electric Chiller Model

The electric chiller model used in this study was adapted from the model developed by Liu for a high efficiency 1000 ton centrifugal chiller. The modeled components of the chiller are the compressor, the evaporator, and the condenser. For proprietary reasons, any references to the manufacturer or equipment model number have been excluded.

Table 3.1 lists the electric chiller manufacturer's data at different conditions. In the first column, Load represents the building cooling load in tons. The manufacturer lists conditions from a part load of 400 tons up to a maximum load of 1000 tons (40% to 100% load). The temperature of the cooling water entering the condenser, Tcnd,in, and the temperature of the chilled water exiting the evaporator, Tevp,out, are specified conditions. The third and fourth columns of the table labeled gpmcnd and gpmevp represent the volume flow rates of cooling water through the condenser and chilled water through the evaporator respectively. The final three columns show the chiller performance for each of these conditions. Wcmp is the electrical power input required by the compressor in kilowatts, and Tcnd and Tevp are the saturation temperatures of the condenser and evaporator respectively.


Table 3.1: Chiller Manufacturer Data
Load
Tcnd,in
Tevp,out
gpmcnd
gpmevp
Wcmp
Tcnd
Tevp
1000
85
44
3000
2400
538
96.95
40.99
900
85
44
3000
2400
463
95.67
41.15
800
85
44
3000
2400
406
94.45
41.30
700
85
44
3000
2400
352
93.23
41.46
600
85
44
3000
2400
302
92.04
41.61
500
85
44
3000
2400
259
90.87
41.76
1000
75
44
3000
2400
455
86.77
40.99
900
75
44
3000
2400
402
85.55
41.15
800
75
44
3000
2400
350
84.33
41.30
700
75
44
3000
2400
304
83.14
41.46
600
75
44
3000
2400
261
81.96
41.61
500
75
44
3000
2400
222
80.79
41.76
400
75
44
3000
2400
185
79.65
41.91
 

Compressor

The current compressor model has been adapted from two previous compressor models. Weber (1988) developed a model which involved the use of an ideal Carnot efficiency combined with isentropic and compressor load efficiency factors. Liu (1997) updated this model by using the more recent manufacturer's data given in Table 3.1.

The compressor model was used to predict compressor electrical power input as a function of evaporator and condenser saturation temperatures at various loads. First, the equation for Carnot efficiency is used:

(3.1)

where  is the electrical power input to the compressor and  is the cooling load. It was assumed that an additional amount of chiller energy was required to overcome friction forces. Therefore, the actual electrical power required by the compressor, , was determined to be:

(3.2a)

where  is the ideal compressor power input found in the Carnot efficiency equation and  is the irreversible power made up of two parts: a fraction, f, of  and a friction term, . Equation 3.2a becomes:

(3.2b)

To obtain this actual compressor power input, the experimental compressor power (given in Table 3.1) was plotted against the ideal compressor power from the Carnot efficiency equation, and a curve fit was produced. Figure 3.1 shows this model which gives an equation for the actual compressor power, in kilowatts, dependent only on the ideal compressor power. The equation, in the form of Equation 3.2a and 3.2b, is: 

(kW) (3.3)

Figure 3.1: Chiller Model


A 500 ton electric chiller was also modeled to use in combination with each of the gas chillers for a hybrid system. The equations used to model the compressor for the 500 ton chiller were similar to the above equations. They were scaled to apply to the smaller chiller.

Evaporator

The same approach taken by Weber and Liu was again used in the current study for the heat exchange properties of the evaporator and condenser. Weber describes in detail the development of the UA equations for both the evaporator and condenser. The following equations were used to model the evaporator's performance:

(3.4)

  (3.5)

(3.6)

(3.7)

where is again the building cooling load converted from tons to Btu/hris the mass flow rate of the chilled water flowing through the evaporator in lb/hr, Cpw is the constant pressure specific heat of water (assumed to be 1 Btu/(lb-R)), Twevpi and Twevpo are the evaporator entering and exiting water temperatures in R respectively, UAevp is the overall conductance of the evaporator in Btu/(hr-R), and LMTDevp is the log mean temperature difference for the evaporator.

The above equations were applied to the manufacturer's data for a 1000 ton chiller to produce Figure 3.2 below and to give the following UA equation for the evaporator:

(3.8)

This equation is a function of the cooling load and has the units Btu/hr-R; therefore, UA varies with the building cooling load which here is only a function of outside dry bulb temperature. 

Figure 3.2: UAevp Vs. Cooling Load



For the 500 ton electric chiller, the UA equations for the evaporator were scaled so that a 500 ton electric chiller could be used in combination with each of the gas chillers in a hybrid system and with another 500 ton electric chiller.

Condenser

Liu and Weber used a similar approach to model the condenser, but here, instead of the LMTD method, an Effectiveness-NTU method was used to model the heat exchange equations of the condenser. As a result of the iterative procedures between the inlet and exit temperatures of the condenser and cooling tower, this method was preferred. The following equations were used to model the condenser's performance:

(3.9)

(3.10)

where is the heat rejected from the condenser in Btu/hr is the mass flow rate of water through the condenser in lb/hr, and Twcndi and Twcndo are the condenser entering and exiting water temperatures respectively.

Then the Effectiveness-NTU method was applied. The effectiveness, e, is unitless and is defined as the ratio of the actual heat transfer rate to the maximum possible heat transfer rate. For a counterflow heat exchanger, the equation for effectiveness is:

(3.11)

where Cr, the heat capacity ratio, in this case is defined as:

(3.12)

Equation 3.11 reduces to the following equation.

(3.13)

The number of transfer units (NTU) is a dimensionless parameter that is widely used for heat exchanger analysis. For this study, it is defined below as:

(3.14)

where UAcnd is the overall conductance of the condenser. Finally, the heat transfer equation for the condenser was defined in terms of effectiveness.

(3.15)

From the manufacturer's data, the UA equation for the condenser was determined to be a function of the cooling load as seen in Figure 3.3 and in the following equation:

(3.16)

for a load less than or equal to 800 tons, and

(3.17)

for a cooling load greater than 800 tons. 

Figure 3.3: UAcnd Vs. Cooling Load


For the 500 ton electric chiller, the UA equations for the condenser were scaled appropriately.

Gas Chiller Models

Three types of natural gas chillers were considered for this study: a single stage absorption chiller, a double stage absorption chiller, and a natural gas engine driven chiller.

Single Stage Absorption Chiller

Manufacturer's performance data was obtained for a 1000 ton single stage absorption chiller. Through a calculation process described in the manufacturer's catalog, in which design conditions of a 85oF entering cooling water temperature and a 44oF chilled water temperature were used, it was determined that the full load steam rate to the absorber was 19.4 lbs/hr-ton. Therefore, for the 1000 ton machine, the full load steam consumption is 19,400 lbs/hr.

To determine the part load steam consumption at different conditions, a load percent was calculated by dividing the building cooling load, determined from the building cooling load profile, by the total design tons, 1000 tons.

(3.18)

From manufacturer's performance data listed and charted in the catalog, the following graph was developed. Figure 3.4 plots the percent of design energy input against the load percent calculated above for various entering cooling water temperatures. 

Figure 3.4: Part Load Performance for Single Stage Absorber
Percent of Design Energy Input Vs. Percent of Design Load at Varying Entering Cooling Water Temperatures



Using this graph, part load steam rates could be determined by multiplying the full load steam rate, 19.4 lbs/hr-ton, by the percent of design energy input.

One assumption made was that the steam pressure at the chiller steam input point is 12 psig. At 12 psig, the latent heat of vaporization is 975 Btu/lbm. Multiplying this value by the part load steam rate yields the steam heat transfer rate per ton. A boiler efficiency of 0.78 was also assumed (ASHRAE, 1996).

These equations were scaled to model a 500 ton single stage absorption chiller to be used in combination with the 500 ton electric chiller for a hybrid system.

Double Stage Absorption Chiller

A very similar method was used in modeling a 1000 ton double stage absorption chiller. Manufacturer's data was obtained and the same design conditions of 85oF entering cooling water and 44oF leaving chilled water were used. Through a similar calculation process specified by the manufacturer, the full load steam rate was determined to be 9.8 lbs.hr-ton. Therefore, the full load steam consumption for the 1000 ton double stage absorption chiller is 9800 lbs/ton.

A load percent was calculated again by dividing the building cooling load by the total design tons. From the manufacturer's performance data, the following graph was developed. Figure 3.5 plots the percent of design energy input against the load percent calculated above for various entering cooling water temperatures. 

Figure 3.5: Part Load Performance for Double Stage Absorber
Percent of Design Energy Input Vs. Percent of Design Load at Varying Entering Cooling Water Temperatures



Using this graph, part load steam rates could be determined by multiplying the full load steam rate, 9.8 lbs/hr-ton, by the percent of design energy input.

An assumption was made that the steam pressure at the generator is 115 psig. At 115 psig, the latent heat of vaporization is 880 Btu/lbm. Multiplying this value by the part load steam rate yields the steam heat transfer rate per ton. A boiler efficiency of 0.78 was also assumed.

These equations were scaled to model a 500 ton double stage absorption chiller to be used in combination with the 500 ton electric chiller for a hybrid system.

Gas Engine Driven Chiller

The engine driven chiller considered in this study has a single turbocharged engine driving a screw compressor. Manufacturer's data for this chiller was obtained in a slightly different form. From the data, Figure 3.6 was developed. Again, a load percent was calculated from the building cooling load profile. The graph plots coefficient of performance against the percent of design load for varying entering cooling water temperatures.

Figure 3.6: Part Load Performance
Coefficient of Performance Vs. Percent of Design Load at Varying Entering Cooling Water Temperatures


Using this graph, the COP is determined for the respective conditions. The cooling load is divided by the COP to determine the heat input, Qgas, to the engine. An engine thermal efficiency, heng, was approximated at 30% (Taylor, 1996), so that the amount of work used by the compressor is determined by the following equation:

(3.19)

Then, the condenser heat rejection, Qcnd, was then calculated by:

(3.20)

The equations used to model the 1000 ton engine driven chiller were scaled to model a 500 ton engine driven chiller to be used in combination with 1) the 500 ton electric chiller for a hybrid system and 2) another 500 ton gas engine driven chiller.

Engine Heat Recovery
As an option, heat may be recovered from the engine jacket and exhaust system from the gas engine driven chiller to be used by the consumer for domestic hot water or process load. This is an excellent economic bonus for a site which has a hot water demand. From before, the heat input was determined using Figure 3.6. Performing an energy balance on the engine,

(3.21)

where QWH is the waste heat rejected from the engine. Since Wcmp is found by Equation 3.19 above, QWH can be calculated by:

(3.22)

From the manufacturer's catalog, it is determined that only a fraction of this waste heat can be recovered. The manufacturer gives a value for this fraction, hWH, of 0.65 for the engines for both the 500 ton and 1000 ton engine driven chiller. Therefore, the amount of engine heat that can be recovered and used for the hot water demand is:

(3.23)

The decreased boiler gas usage, Qgas,credit, due to this recovered engine heat is then found by:

(3.24)

where hboiler is the boiler efficiency. This number, when natural gas rates are applied, is the amount that the site can save on gas for hot water demand. In this study, this cost is credited back to the chiller system's energy cost.