E hhxi E hxo

where m is the mass flow rate and x is mass concentration of LiBr in the solution. The first law of thermodynamics yields the energy balance of each component of the absorption system as follows:

An overall energy balance of the system requires that the sum of the generator, evaporator, condenser, and absorber heat transfer must be 0. If the absorption system model assumes that the system is in a steady state and that the pump work and environmental heat losses are neglected, the energy balance can be written as

The energy, mass concentrations, and mass balance equations of the various components of an absorption system are given in Table 6.2 (Kizilkan et al., 2007). The equations of Table 6.2 can be used to estimate the energy, mass concentrations, and mass balance of a LiBr-water system. In addition

Table 6.2 Energy and Mass Balance Equations of Absorption System Components

System components

Mass balance equations

Energy balance equations

Pump

w = th2h2 — hh1 hj

Solution heat exchanger

m4 hh5. "4

til2 h + th4h4 = tii3h3 + mth;,

Solution

hi 5 = hi 6, x5 = x6

h = h6

expansion valve

Absorber

h = rh6 + rh10 + rh11

rn1x1 = rh6 x6 + rh10 x10 + hh11x11

Qa = rn6h6 + til 1oh1o + ^1^11 - til h

hh 3 x3 hh 4 x4 h x7

Qg = th4h4 + hh7 h — tii3h3

Condenser

h hh g, x7 xg

QC = hh7h7 - hhghg

Refrigerant expansion valve

Wlft hh 9, xg x9

hg = hg

Evaporator

hh9 til 10 ^ hh11' x9 x10

Qe = th10hJ0 + th11hJ1 - hh9h9

to these equations, the solution heat exchanger effectiveness is also required, obtained from (Herold et al., 1996):

The absorption system shown in Figure 6.23 provides chilled water for cooling applications. Furthermore, the system in Figure 6.23 can also supply hot water for heating applications, by circulating the working fluids in the same fashion. The difference of operation between the two applications is the useful output energy and the operating temperature and pressure levels in the system. The useful output energy of the system for heating applications is the sum of the heat rejected from the absorber and the condenser while the input energy is supplied to the generator. The useful output energy of the system for the cooling applications is heat extracted from the environment by the evaporator while the input energy is supplied to the generator (Alefeld and Radermacher, 1994; Herold et al., 1996).

The cooling coefficient of performance of the absorption system is defined as the heat load in the evaporator per unit of heat load in the generator and can be written as (Herold et al., 1996; Tozer and James, 1997):

COP ■ = = m10h10 + m11h11 ~ rh9h9 = m18(h18 - h19) (6 73)

where h = specific enthalpy of working fluid at each corresponding state point (kJ/kg).

The heating COP of the absorption system is the ratio of the combined heating capacity, obtained from the absorber and condenser, to the heat added to the generator and can be written as (Herold et al., 1996; Tozer and James, 1997):

COP . = QC + QA = (h7h7 - mM + (h6h6 + hh 10h10 + h11h11 ~ hh1h1) luting q^ hn4h4 + m7h7 - hh

Therefore, from Eq. (6.71), the COP for heating can be also written as

qg qg

Equation (6.75) shows that the heating COP is in all cases greater than the cooling COP.

The second-law analysis can be used to calculate the system performance based on exergy. Exergy analysis is the combination of the first and second laws of thermodynamics and is defined as the maximum amount of work potential of a material or an energy stream, in relation to the surrounding environment (Kizilkan et al., 2007). The exergy of a fluid stream can be defined as (Kotas, 1985; Ishida and Ji, 1999):

where e = specific exergy of the fluid at temperature T (kJ/kg).

The terms h and s are the enthalpy and entropy of the fluid, whereas h0 and s0 are the enthalpy and entropy of the fluid at environmental temperature T0 (in all cases absolute temperature is used in Kelvins).

The availability loss in each component is calculated by

where AE = lost exergy or irreversibility that occurred in the process (kW).

The first two terms of the right-hand side of Eq. (6.77) are the exergy of the inlet and outlet streams of the control volume. The third and fourth terms are the exergy associated with the heat transferred from the source maintained at a temperature, T. The last term is the exergy of mechanical work added to the control volume. This term is negligible for absorption systems because the solution pump has very low power requirements.

FIGURE 6.26 Availability flow balance of the absorption system.

The equivalent availability flow balance of the system is shown in Figure 6.26 (Sencan et al., 2005). The total exergy loss of absorption system is the sum of the exergy loss in each component and can be written as (Talbi and Agnew, 2000):

The second-law efficiency of the absorption system is measured by the exergetic efficiency, r|ex, which is defined as the ratio of the useful exergy gained from a system to that supplied to the system. Therefore, the exergetic efficiency of the absorption system for cooling is the ratio of the chilled water exergy at the evaporator to the exergy of the heat source at the generator and can be written as (Talbi and Agnew, 2000; Izquerdo et al., 2000):

The exergetic efficiency of absorption systems for heating is the ratio of the combined supply of hot water exergy at the absorber and condenser to the exergy of the heat source at the generator and can be written as (Lee and Sherif, 2001; Qengel and Boles, 1994):

DESIGN OF SINGLE-EFFECT LiBr-WATER ABSORPTION SYSTEMS

To perform estimations of equipment sizing and performance evaluation of a single-effect water-lithium bromide absorption cooler, basic assumptions and input values must be considered. With reference to Figures 6.23-6.25, usually the following assumptions are made:

1. The steady-state refrigerant is pure water.

2. There are no pressure changes except through the flow restrictors and the pump.

3. At points 1, 4, 8, and 11, there is only saturated liquid.

4. At point 10, there is only saturated vapor.

5. Flow restrictors are adiabatic.

6. The pump is isentropic.

7. There are no jacket heat losses.

A small 1 kW unit was designed and constructed by co-workers and the author (Florides et al., 2003). To design such a system, the design (or input) parameters must be specified. The parameters considered for the 1 kW unit are listed in Table 6.3.

The equations of Table 6.2 can be used to estimate the energy, mass concentrations, and mass balance of a LiBr-water system. Some details are given in the

Table 6.3 Design Parameters for the Single-Effect Water-Lithium Bromide Absorption Cooler

Parameter

Symbol

Value

Capacity

QE

1.0 kW

Evaporator temperature

Tio

6°C

Generator solution exit temperature

T4

75°C

Weak solution mass fraction

x1

55 % LiBr

Strong solution mass fraction

X4

60 % LiBr

Solution heat exchanger exit temperature

T3

55°C

Generator (desorber) vapor exit temperature

70°C

Liquid carryover from evaporator

™11

0.025 rh10

following paragraphs so the reader will understand the procedure required to design such a system.

Since, in the evaporator, the refrigerant is saturated water vapor and the temperature (T10) is 6°C, the saturation pressure at point 10 is 0.9346kPa (from steam tables) and the enthalpy is 2511.8 kJ/kg. Since, at point 11, the refrigerant is a saturated liquid, its enthalpy is 23.45 kJ/kg. The enthalpy at point 9 is determined from the throttling process applied to the refrigerant flow restrictor, which yields h9 = h8. To determine h8, the pressure at this point must be determined. Since, at point 4, the solution mass fraction is 60% LiBr and the temperature at the saturated state is assumed to be 75°C, the LiBr-water charts (see ASHRAE, 2005) give a saturation pressure of 4.82 kPa and h4 = 183.2 kJ/kg. Considering that the pressure at point 4 is the same as in 8, h8 = h9 = 131.0 kJ/kg (steam tables). Once the enthalpy values at all ports connected to the evaporator are known, mass and energy balances, shown in Table 6.2, can be applied to give the mass flow of the refrigerant and the evaporator heat transfer rate.

The heat transfer rate in the absorber can be determined from the enthalpy values at each of the connected state points. At point 1, the enthalpy is determined from the input mass fraction (55%) and the assumption that the state is a saturated liquid at the same pressure as the evaporator (0.9346kPa). The enthalpy value at point 6 is determined from the throttling model, which gives h6 = h5.

The enthalpy at point 5 is not known but can be determined from the energy balance on the solution heat exchanger, assuming an adiabatic shell, as follows:

The temperature at point 3 is an input value (55°C) and since the mass fraction for points 1 to 3 is the same, the enthalpy at this point is determined as 124.7 kJ/kg. Actually, the state at point 3 may be a sub-cooled liquid. However, at the conditions of interest, the pressure has an insignificant effect on the enthalpy of the sub-cooled liquid and the saturated value at the same temperature and mass fraction can be an adequate approximation.

The enthalpy at state 2 can be determined from the equation for the pump shown in Table 6.2 or from an isentropic pump model. The minimum work input (w) can therefore be obtained from:

In Eq. (6.82), it is assumed that the specific volume (v, m3/kg) of the liquid solution does not change appreciably from point 1 to point 2. The specific volume of the liquid solution can be obtained from a curve fit of the density (Lee et al., 1990) and noting that v = 1/p:

p = 1145.36 + 470.84x + 1374.79x2 - (0.333393 + 0.571749x)(273 + T)

This equation is valid for 0 < T < 200°C and 20 < x < 65%.

Table 6.4 LiBr-Water Absorption Refrigeration System Calculations Based on a Generator Temperature of 75°C and a Solution Heat Exchanger Exit Temperature of 55°C

Point

h (kJ/kg)

m (kg/s)

P (kPa)

T (°C)

%LiBr (x)

Remarks

1

83

0.00517

0.93

34.9

55

2

83

0.00517

4.82

34.9

55

3

124.7

0.00517

4.82

55

55

Sub-cooled liquid

4

183.2

0.00474

4.82

75

60

5

137.8

0.00474

4.82

51.5

60

6

137.8

0.00474

0.93

44.5

60

7

2612.2

0.000431

4.82

70

0

Superheated steam

8

131.0

0.000431

4.82

31.5

0

Saturated liquid

9

131.0

0.000431

0.93

6

0

10

2511.8

0.000421

0.93

6

0

Saturated vapor

11

23.45

0.000011

0.93

6

0

Saturated liquid

Description

Symbol

kW

Capacity (evaporator output power)

Qs

1.0 kW

Absorber heat, rejected to the environment

Qa

1.28 kW

Heat input to the generator

Qg

1.35 kW

Condenser heat, rejected to the environment

Qc

1.07 kW

Coefficient of performance

COP

0.74 kW

The temperature at point 5 can be determined from the enthalpy value. The enthalpy at point 7 can be determined, since the temperature at this point is an input value. In general, the state at point 7 is superheated water vapor and the enthalpy can be determined once the pressure and temperature are known.

A summary of the conditions at various parts of the unit is shown in Table 6.4; the point numbers are as shown in Figure 6.23.

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