Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
351
1 49 0 07969
1 1
21 1 127
6360
. .
T F
. w
⎛ ⎞
= −
⎜ ⎟
⎜ ⎟
⎝ ⎠
6
1 49 0 07969
2 2
22 1 127
6360
. .
T F
. w
⎛ ⎞
= −
⎜ ⎟
⎜ ⎟
⎝ ⎠
7
1 49 0 07969
8 8
28 1 127
6360
. .
T F
. w
⎛ ⎞
= −
⎜ ⎟
⎜ ⎟
⎝ ⎠
8 Temperature and humidity ratio is known at point 1,
and by using 1, the constant F11 can be calculated and the line connecting 1-2 is fixed. This can also be done for
line 3-4, because point 3 is fixed, and therefore F12 can be calculated. The other two lines, connecting 2-3 F22
and 1-4 F28 can be calculated in the same way.
The actual performance of the wheel shifts from statepoint 2 to statepoint 2
A
. Two effectiveness values ef1 and ef2 are used to calculate the actual outlet state
2. The dashed lines in Fig. 2 can calculated based on new F12, F22 with the actual thermodynamic properties
of air in statepoint 2 and replacing the old values from 4, 7.
An iteration based on Newton Raphson method is used to find intersection of those lines. This intersection
fixes the outlet condition at the process side. The intersection of the two lines indicates the actual outlet
condition at the process side. The outlet conditions at the regeneration side can easily be calculated based on
conservation of mass and energy, 9, 10:
4 2
1 3
reg proc
proc reg
m w
m w
m w
m w
+ =
+
9
1 3
2 4
proc reg
proc reg
m h
m h
m h
m h
+ =
+
10 Required values of [ef1, ef2] = [a, b] are set, which
correspond to efficiency according to the dehumidification mode of the wheel. For enthalpy
exchange mode the above efficiencies are set [ef1, ef2] = [0.9, 0.9] while for active dehumidification mode the set
of efficiencies takes the values [ef1, ef2] = [0.16, 0.73].
The effectiveness values are calibrated using the measurements the desiccant cooling unit powered by 10
m
2
of flat plate solar liquid collectors is implemented for air-conditioning a room in the Park of Energy Awareness
PENA in Lavrio as well as from Klingenburg model [4]. The system uses a Lithium Chloride sorption wheel
and is optimized to work with auxiliary heat regeneration source.
IV. Enthalpy Exchange Wheel
Performance Passive Sorption Wheel
The results of the developed model in Mathcad [5] for passive sorption wheels with the set of efficiencies [ef1,
ef2] = [0.9, 0.9] are compared with the outputs of Klingenburg software [4] for SECO sorption wheel.
TABLE I
C
OMPARISON
O
F
M
ANUFACTURERS
S
OFTWARE
A
ND
T
HE
D
EVELOPED
M
ODEL
I
N
M
ATHCAD
S
OFTWARE
Entrance conditions SECO
wheel Mathcad model
Process Air Regeneration
Air Outlet Process Air
Statepoint 2 Outlet Process Air
Statepoint 2 T
[
o
C] W
[gkg] T
[
o
C] W
[gkg] T
[
o
C] W
[gkg] T
[
o
C] W
[gkg] 20 10.2 65 12.5 53.8 11.3 54.1 10.9
25 12.9 65 15.7 54.5 13.1 54.9 12.8 30 13.3 70 15.7 57.6 12.9 58.2 12.1
35 17.8 70 21.8 58.9 19.5 56.1 18.7 40 23.5 70 30.1 59.3 21.4 57.4 19.4
V. Desiccant Wheel Performance
Active Sorption Wheel
In the present paper, a useful correlation model is also presented to evaluate the performance of an active rotary
LiCl desiccant wheel based on ventilation cycle. The model has been derived from the interpolation of
experimental data [6] obtained from the experimental setup, while the correlations have been developed for
predicting outlet temperature and humidity ratio of the process and regeneration air streams of the wheel. In Fig.
3 real time measurements of moisture removal capacity DW of the wheel are presented.
Fig. 3. Moisture Removal Capacity w
1
-w
2
of the active wheel
The performance of an active sorption wheel is dependent upon four parameter groups, which will be
mentioned as performance indicators: mass flow rate parameters, process air inlet to the wheel parameters
and regeneration air inlet to the wheel parameters [7].
All the proposed indicators are intrinsic because the performance of a sorption wheel depends on outdoor and
regeneration conditions as well as the ratio of mass flow rates of the process and regeneration streams. These four
parameter groups include six parameters. The effect of these parameters on the wheel is not uniform.
As the thermal coefficient of performance of a desiccant system and the moisture removal capacity are
dimensionless parameters, it is desired to reflect the relationship between them and other dimensionless
parameters in the correlation model. In order to establish
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
352 the dimensionless equations, the following six
dimensionless variables were introduced:
1 2
1 proc
w w
DW w
∗
⎛ ⎞
− = ⎜
⎟ ⎝
⎠
11
3 1
3 inr
T T
T T
∗
⎛ ⎞
− = ⎜
⎟ ⎝
⎠
12
4 3
3 reg
w w
DW w
∗
⎛ ⎞
− = ⎜
⎟ ⎝
⎠
13
2 1
2 proc
T T
T T
∗
⎛ ⎞
− = ⎜
⎟ ⎝
⎠
14
3 4
4 regout
T T
T T
∗
⎛ ⎞
− = ⎜
⎟ ⎝
⎠
15
proc reg
m ratiom
m =
16
V.1. Influence of Inlet Air Temperatures in Process
and Regeneration Air Streams on Moisture Removal Capacity
The following equations are suggested, with considerable accuracy, in order to estimate the influence
of the ratio of mass flow rates and inlet air temperatures on dimensionless Moisture Removal Capacity,
proc
DW
∗
:
1
1
a
ratiom proc
proc
f DW
DW
∗ ∗
=
17
1
1
b
ratiom inr
inr
z T T
∗ ∗
=
18 To estimate the function between
1 proc
f DW
∗
and
1 inr
z T
∗
by means of regression techniques, the following potential linear model was assumed:
1 1
1 1
proc inr
f DW
A z T B
∗ ∗
= ⋅ +
19 In Eqs. 17, 18 and 19,
a
1
, b
1
, A
1
, B
1
are constants to be determined by fitting and obtained by regression of
Eq. 19 based on measurements. The dimensionless parameters
a
1
and b
1
were computed with the criterion of minimizing the root mean
square error RMSE. The procedure leads to the following
equation, with acceptable correlation indexes of R
2
= 0.96409 and
RMSE = 3.29.
Fig. 4. Dimensionless moisture removal capacity
The values of a
1
and b
1
are 1.84 and 2.12 respectively while the values of
A
1
and B
1
are 0.8225 and 9.6710
-4
respectively. From the above set of Equations 17, 18, 19 the
humidity ratio w
2
at the outlet of the wheel in the process stream can be evaluated when
T
1
, T
3
and the ratio of mass flow rates are known.
V.2. Influence of Moisture Removal Capacity on Air
Temperatures before and after Dehumidification The following equations are suggested in order to
express accurately the influence of the ratio of mass flow rates and the dimensionless moisture removal capacity
on air temperatures of process air stream before and after dehumidification,
proc
T
∗
:
2
2
a
ratiom proc
proc
f T
T
∗ ∗
= 20
2
2
b
ratiom proc
proc
z DW
DW
∗ ∗
= 21
To estimate the function between
2 proc
f T
∗
and
2 proc
z DW
∗
by means of regression techniques, the following potential linear model was assumed:
2 2
2 2
proc proc
f T
A z
DW B
∗ ∗
= ⋅ + 22
In Eqs. 20, 21 and 22, a
2
, b
2
, A
2
, B
2
are constants to be determined by fitting and obtained by regression of
Eq. 22 based on measurements. The dimensionless parameters
a
2
and b
2
were computed with the criterion of minimizing the root mean
square error RMSE. The procedure leads to the following
equation, with acceptable correlation indexes of R
2
= 0.9575 and
RMSE = 5.57.
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
353 The values of a
2
and b
2
are 3.45 and 4.22 respectively while the values of
A
2
and B
2
are 0.93742 and -0.01558 respectively.
Fig. 5. Dimensionless outlet process wheel temperature
From the above set of Eqs. 20, 21, 22 the dry bulb temperature
T
2
at the outlet side of the process stream of the wheel can be evaluated when
w
1
, w
2
and the ratio of mass flow rates are known.
V.3. Influence of Inlet Air Temperatures in Process
and Regeneration Air Streams The following equations are suggested in order to
express accurately the influence of the ratio of mass flow rates and outdoor air temperature on inlet and outlet
temperatures of the regeneration air stream:
3
3
a
ratiom regout
regout
f T
T
∗ ∗
=
23
3
3
b
ratiom inr
inr
z T T
∗ ∗
=
24 To estimate the function between
3 regout
f T
∗
and
3 inr
z T
∗
by means of regression techniques, the following potential linear model was assumed:
3 3
3 3
3 regout
inr
f T
A B
z T
∗ ∗
= + ⋅
25 In Eqs. 23, 24 and 25,
a
3
, b
3
, A
3
, B
3
, C
3
, D
3
are constants to be determined by fitting and obtained by
regression of Eq. 25 based on measurements. The dimensionless parameters
a
3
and b
3
were computed with the criterion of minimizing the root mean
square error RMSE. The procedure leads to the following
equation, with acceptable correlation indexes of R
2
= 0.9606 and
RMSE = 4.538.
Fig. 6. Dimensionless regeneration temperature
The values of a
3
and b
3
are 2.97 and 3.59 respectively while the values of
A
3
, B
3
, are -0.01937 and 0.8303 respectively.
From the above set of Eqs. 23, 24, 25 the dry bulb temperature
T
4
at the outlet side of the regeneration stream of the wheel can be evaluated when
T
1
, T
3
and the ratio of mass flow rates are known.
V.4. Influence of Moisture Removal Capacity on
Humidity Ratio at Wheel’s Outlet Regeneration Stream
The following equations are suggested in order to express accurately the influence of the ratio of mass flow
rates and the moisture removal capacity on wheel’s outlet regeneration stream:
4
4
a
ratiom reg
reg
f DW
DW
∗ ∗
=
26
4
4
b
ratiom proc
proc
z DW
DW
∗ ∗
=
27 To estimate the function between
4 reg
f DW
∗
and
4 proc
z DW
∗
by means of regression techniques, the following potential third degree polynomial model was
assumed:
4 4
4 4
reg proc
f DW
A B
z DW
∗ ∗
= + ⋅
28 In Eqs. 26, 27 and 28,
a
4
, b
4
, A
4
, B
4
, are constants to be determined by fitting and obtained by regression of
Eq. 28 based on measurements. The dimensionless parameters
a
4
and b
4
were computed with the criterion of minimizing the root mean
square error RMSE. The procedure leads to the following
equation, with acceptable correlation indexes of R
2
= 0.9328 and
RMSE = 6.76.
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
354
Fig. 7. Dimensionless moisture removal at the regeneration stream
The values of a
4
and b
4
are 1.77 and 1.49 respectively while the values of
A
4
, B
4
, are -0.05381, 1.3619. From the above set of Eqs 26, 27, 28 the Humidity ratio at
state point 4 can be evaluated when w
1
, w
2
and T
3
, T
4
are known.
VI. Conclusion
