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, T_{cnd,in},
and the temperature of the chilled water exiting the evaporator, T_{evp,out},
are specified conditions. The third and fourth columns of the table labeled
gpm_{cnd} and gpm_{evp} 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. W_{cmp} is the electrical
power input required by the compressor in kilowatts, and T_{cnd}
and T_{evp} are the saturation temperatures of the condenser
and evaporator respectively.
















































































































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:
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:
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:
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:
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.
where is again the building cooling load converted from tons to Btu/hr, is the mass flow rate of the chilled water flowing through the evaporator in lb/hr, C_{pw} is the constant pressure specific heat of water (assumed to be 1 Btu/(lbR)), T_{wevpi}_{ }and T_{wevpo} are the evaporator entering and exiting water temperatures in R respectively, UA_{evp} is the overall conductance of the evaporator in Btu/(hrR), and LMTD_{evp} 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:
This equation is a function of the cooling load and has the units Btu/hrR;
therefore, UA varies with the building cooling load which here is only
a function of outside dry bulb temperature.
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 T_{wcndi} and T_{wcndo} are the condenser entering and exiting water temperatures respectively.
Then the EffectivenessNTU 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:
where C_{r}, the heat capacity ratio, in this case is defined as:
Equation 3.11 reduces to the following equation.
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:
where UA_{cnd} is the overall conductance of the condenser. Finally, the heat transfer equation for the condenser was defined in terms of effectiveness.
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:
for a load less than or equal to 800 tons, and
for a cooling load greater than 800 tons.
For the 500 ton electric chiller, the UA equations for the condenser were
scaled appropriately.
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.
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.
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.
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.
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.
Using this graph, the COP is determined for the respective conditions.
The cooling load is divided by the COP to determine the heat input, Q_{gas},
to the engine. An engine thermal efficiency, h_{eng},
was approximated at 30% (Taylor, 1996), so that the amount of work used
by the compressor is determined by the following equation:
Then, the condenser heat rejection, Q_{cnd}, was then calculated by:
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.
where Q_{WH} is the waste heat rejected from the engine. Since W_{cmp} is found by Equation 3.19 above, Q_{WH }can be calculated by:
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, h_{WH}, 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:
The decreased boiler gas usage, Q_{gas,credit}, due to this recovered engine heat is then found by:
where h_{boiler} 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.