CAPÍTULO II. MEDIDAS EN MATERIA DE SANCIONES
DISPOSICIONES ADICIONALES
C1. Absorption chillers and heat pumps
The heat exchanger balances noted in Section B are easily applied to the 4 heat exchangers in an absorption machine:
Q mCE T T mCE E T T j j j j j j j j = ± - = ± - -
a f d
ini a f d
outi
1 (5.9) where the subscript j substitutes for generator, condenser, absorber or evaporator; and the ± sign preserves our definition that Qj be positive. Substituting Equation (5.9) for each of the 4 heat exchangers into Equation (4.28) (i.e., eliminating refrigerant temperatures in favor of coolant temperatures), one obtains a performance equation that is even more ungainly than Equation (5.3), not to mention the fact that more parameters are involved and must be determined in order to implement the model.We can simplify the analysis slightly by exploiting approximations based on the relative magnitudes of several of the terms, as originally pointed out in [Chua et al 1997]. However, a formula as simple as Equation (5.5) does not follow. So even the nominally simplified re- sults here are limited to optimization studies of the type to be presented in Chapter 9. (A quasi-empirical chiller model which offers a limited predictive and diagnostic capability for absorption chillers will be de- veloped in Chapter 10.)
First, for properly-operating commercial absorption units, the heat leaks at the absorber and condenser are negligible. So we retain heat leak terms only at the generator and evaporator. Second, we treat the fraction ξ of total heat rejection Qreject effected at the condenser as a control variable. As we’ll see in Chapter 9, one particular partition- ing of the heat rejection maximizes system COP.
Third, heat exchange at the generator is usually latent, rather than sensible, so the generator energy balance can be written in terms of the heat exchanger’s thermal conductance UA:
Qgen =
a f d
UA gen Tgenin -Tgeni
. (5.10) When heat exchange at the generator is dominated by sensible heat, as in water-fired units, Equation (5.9) is retained.Unlike the heat exchangers in mechanical chillers, the heat exchangers in absorption chillers can have a non-negligible variation in their UA
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value along the heat exchanger. This is caused by the change in solu- tion concentration (and the change in solution temperature that is uniquely linked to the concentration effect) as it traverses the heat exchanger. Rigorous thermodynamic modeling should take this effect into account. However it would probably obviate the possibility of emerging with the types of simple analytic formulae derived here for chiller performance. In the approximate models developed here, we treat the UA value of the heat exchangers in absorption machines as constant at their process-average value. For current commercial absorption units, the errors introduced by this approximation are typically of the same magnitude as experimental measurement uncertainties.
Fourth, in many commercial absorption chillers and heat pumps, the absorber and condenser are connected by a single stream of coolant that flows first through the absorber and then through the condenser. In this instance, Tcondin is additionally constrained by
T T Q mC T Q mC abs cond in abs in abs abs abs in reject = +
a f
= +b g
1a f
-x . (5.11) However, the finite capacity (mC)abs of the coolant stream is occasionally ignored in the analysis. To ensure a meaningful comparison between model and experiment in this case, one simply adopts an infinitely large value for (mC)abs in the calculation.C2. Absorption heat transformers
As for absorption chillers and heat pumps, several simplifications can be noted for absorption heat transformers. First, the heat leak from the condenser is usually negligibly small because of the relatively small temperature difference with its environment (and the heat leak at the evaporator assumes a change in sign due to the different mode of op- eration). Second, a control variable in heat transformer design (as opposed to heat transformer operation once it is built) is the fraction ψ of the total heat input that is accepted at the generator
y =
+
Q
Q
Q
gen gen evap.
(5.12)Third, heat exchange at the generator and evaporator is usually latent, rather than sensible, so that the heat exchanger energy balances can be written analogously to Equation (5.10):
Qgen=
a f d
UA gen Tgenin -Tgeni
(5.13)Qevap=
a f d
UA evap Tevapin -Tevapi
(5.14)Qabs =
a f d
UA abs Tabs-Tabsini
. (5.15) When heat exchange at the absorber is dominated by sensible heat, as in glycol-cooled heat transformers, Equation (5.9) is retained.C3. Absorption chiller performance curve
By inserting typical realistic values for chiller parameters, one can observe the nature of the characteristic performance curve for absorption machines, as drawn in Figure 5.1. At low values of useful effect, in- ternal dissipation prevails and the curve is linear. This feature is the same as that of mechanical chillers, even though there are additional sources of internal loss. The reason is the approximate constancy of
∆Sint over the operating range of interest. At high values of useful effect, external heat exchanger losses dominate and COP decreases rapidly as useful effect is raised. A maximum COP occurs at the point of optimum tradeoff.
Absorption machines designed to exploit waste heat (a nominally free thermal source) tend to be designed so that their rated capacity lies near the point of maximum useful effect. When one pays for the thermal input,
Figure 5.1 Characteristic performance curve for an absorption machine, plotted as 1/COP against 1/(useful effect), so that the plot pertains to chillers, heat pumps and heat transformers. Note the existence of a point of maximum COP and a point of maximum useful effect.
0
point of maximum COP point of maximum useful effect
1/COP
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as in gas-fired absorption units, the systems are designed so that the rated capacity falls closer to the point of maximum COP. Perhaps not coincidentally, it appears that manufacturers of gas-fired absorption chillers and heat pumps have empirically evolved designs so that the point of maximum useful effect roughly coincides with that of maxi- mum COP.
A key difference between absorption and mechanical devices is that absorption machines exhibit a measurable point of maximum useful effect. This point exists because absorption systems are driven by a thermal, as opposed to an entropy-less, power source. There are two distinct points (values of COP) for each value of useful effect. The upper branch of the characteristic curve in Figure 5.1 is governed by heat-transfer irreversibilities (i.e., the heat exchange bottleneck) in the generator, so COP decreases as useful effect is lowered. Under realistic conditions, the absorption unit should be designed to operate on the higher-COP branch.