Water chillers are commonly employed to chill water for air conditioning systems. This chilled water is circulated thru cooling coils. Air is passed over the coils to be cooled and dehumidified for indoor comfort. The basic components of a water chiller are a compressor and motor, an evaporator, a condenser and assorted piping and controls. In this article we will describe the performance calculations for the basic water chiller thermodynamic cycle.

As an example for our discussion, we will use a compressor with R134a, a flooded evaporator (refrigerant on the shell side) and a shell & tube water cooled condenser also with refrigerant on the shell side. For simplicity of illustration we will assume an 85% efficient centrifugal compressor and no pressure drop in suction or discharge piping. Chilled water enters the evaporator at 54 ^oF and leaves at 44 ^oF. Cooling water enters the condenser at 85 ^oF and leaves at 95 ^oF.

The evaporation is a constant pressure process and the evaporator saturation pressure must be at a temperature colder than the leaving chilled water temperature for the heat transfer to occur. The refrigerant leaves the evaporator shell as a saturated vapor and enters the compressor.

The compressor supplies work to raise the refrigerant to the condenser saturation pressure. The condenser saturation pressure must be higher than the leaving condenser water temperature for heat transfer to occur. The compressor work required is the product of the refrigerant mass flow times the vapor enthalpy at the entrance to the condenser minus the vapor enthalpy leaving the evaporator.

The heat rejected in the condenser is the sum of the heat transferred in the evaporator plus the work input of the compressor. The condensed refrigerant leaves at the condenser saturation pressure, passes thru an expansion device that reduces the pressure to evaporator pressure, and enters the evaporator. In the expansion process, some of the liquid flashes to gas and the refrigerant entering the evaporator is a two phase mixture.

The chilled water is cooled in the evaporator by evaporating the refrigerant. The evaporator heat transfer capacity is equal to the building load. The refrigerant mass flow that must be delivered by the compressor is equal to the building load divided by the difference in enthalpy of the entering and leaving refrigerant conditions.

In the basic cycle, the liquid refrigerant leaves the condenser at its saturation temperature.

The refrigerant properties at various points in the cycle are:

Condenser Saturation Temperature, Tsat=97 ^oF

Evaporator Saturation Temperature, Tsat=42 ^oF

Enthalpy leaving Evaporator, h_g=172.9 Btu/lbm (saturated vapor @ 42 ^oF )

Enthalpy leaving Condenser, h_f=107.8 Btu/lbm (saturated liquid @ 97 ^oF )

Entropy entering Compressor, s_g=0.412 Btu/lbm-R (saturated vapor @ 42 ^oF )

Enthalpy leaving Compressor, h_g=181.3 Btu/lbm (ideal isentropic compression)

Isentropic enthalpy rise due to compression, ∆h_comp=181.3-172.9=8.4 Btu/lbm

Compressor efficiency, Ƞ=0.85

Enthalpy leaving Compressor h_g=172.9+8.4/0.85=182.8 Btu/lbm

From these values several performance parameters of the cycle may be calculated on a per ton basis.

Capacity=12000 Btu/h-ton

Evaporator enthalpy rise=172.9-107.8=65.1 Btu/lbm

Refrigerant mass flow rate=12000/65.1=184.5 lbm/h-ton

Compressor work=184.5*8.4/0.85=1824 Btu/h-ton

= (1824 Btu/h-ton)/(3412 KW-h/BTU)=0.535KW/Ton

In future blogs we will discuss the performance improvements of subcoolers and economizers.

Editor's Note: CR4 would like to thank Jim Larson, GEA Consulting Associate, for contributing this blog entry.