Coefficient of performance and cycle efficiency


The energy for operating the system is applied through the generator, hence the coefficient of performance may be defined as the ratio of the refrigerating effect to the rate of energy supplied to the generator:

COP=l/Hg (14.11)

_ mr(/ive — hlc) mThvg + msghg — msah3

The highest possible coefficient of performance would be obtained by using reversible cycles. Thus, the rate of heat supplied per kilogram of refrigerant (Qg = Hgl mt) to the generator at temperature Tg might be used in a Carnot engine rejecting its heat to a sink at temperature Tc. The efficiency of this engine would be

(Tg — Tc)/Tg = W/Qg

Or

Qg = (TgW)/(Tg-Tc) (14.12)

Where W is the rate of work done, i. e. the area CDEF in Figure 14.4.

Coefficient of performance and cycle efficiency

Entropy kJ/kg K

Fig. 14.4 Temperature-entropy diagram.

If this work is used to drive a Carnot refrigerating machine then the rate of work input to this, the area BCFG, equals W above, and the ratio of areas BCFG and ABGH is

W/Qr=(Tc-Te)/Te

Or

Qv = (TeW)/(Tc — Te) (14ЛЗ)

Where Qr is the refrigerating effect in kW.

Using equations (14.12) and (14.13) an expression for the maximum possible coefficient of performance is obtained:

COPm ax = QJQg

_ (Tg-Tc)Te

(Tc-Te)Tg (14-14)

An improved performance can be achieved by using two generators, the first working at a higher steam pressure and temperature than the second. Vapour from the first generator

Passes to the second where, by condensation, it provides the source of thermal energy.

Coefficients of performance of such double effect machines better than those of machines with single generators are possible and typical values are 0.92 to 1.0, according to ASHRAE (1998).

EXAMPLE 14.6

Calculate the coefficient of performance for the cycle in example 14.5 and compare this with the maximum obtainable.

Answer

From equation (14.11),

COT = 1587 = 050 From equation (14.14),

COP — (347 ~ 305)274 — 1 07 max (305 — 274)347

In practice, the criterion of performance is more commonly the amount of steam required to produce one kW of refrigeration. For the lithium bromide-water cycle the figure is around 0.72 g s-1 kW’1 and about 0.38 g s’1 kW-1 for double effect machines, according to ASHRAE (1998).

Posted in Air Conditioning Engineering


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