a sensitivity analysis of a desiccant wheel

7/27/2019 A Sensitivity Analysis of a Desiccant Wheel

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499 - A Sensitivity Analysis Of A Desiccant Wheel

P. Bourdoukan1*

, E. Wurtz2, P. Joubert

1and M. Sprandio

1

1

LEPTIAB, Universit de La Rochelle La Rochelle, Avenue Marillac, 17000 La Rochelle, France2

Universit de Savoie, Campus Scientifique, 73376 Le Bourget du Lac, France

*Corresponding Author, [email protected]

Abstract

Desiccant cooling powered by solar energy and using water as a refrigerant has a low

environmental impact and appears as an important technique to reduce energy consumption

in buildings. The cooling potential of the system is based on the performance of the

desiccant wheel that removes humidity from outside air to increase the potential of the

humidifier. In this paper a sensitivity analysis of the desiccant wheel dehumidification isperformed using the design of experiments. The impact of outside temperature, outside

humidity ratio, the regeneration temperature and the regeneration humidity ratio is studied

on the dehumidification rate of the wheel using experimental and numerical results.

Keywords: solar desiccant cooling, sensitivity, experiments, simulation

1. Introduction

Solar desiccant cooling is a heat driven technique powered by solar collectors. It is based on

evaporative cooling and utilizes a desiccant wheel to remove humidity from outside air. When

adsorbing the humidity the desiccant needs to be regenerated by moderately hot air stream

provided by solar collectors. This technology presents the advantages of being friendly

environmental since its electrical consumption is limited to the auxiliaries (fans and pumps), beside

it use water as a refrigerant in opposition to vapor compression technique using refrigerants with

high environmental impact. The general scheme of a solar desiccant cooling plant is shown in the

figure 1 below:

Fig. 1. Desiccant cooling installation and evolution of air properties in the psychometric chart

With reference to Fig. 1 the conventional cycle operates as follows: first, outside air (1) is

dehumidified in a desiccant wheel (2); it is then cooled in the sensible regenerator (3) by the return

cooled air before undergoing another cooling stage by an evaporative process (4), finally, it is


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introduced into the building. The operating sequence for the return air (5) is as follows: it is first

cooled to its saturation temperature by evaporative cooling (6) and then it cools the fresh air in the

rotary heat exchanger (7). It is then heated in the regeneration heat exchanger (8) and finally

regenerates the desiccant wheel (9) by removing the humidity before exiting the installation.

The task of the desiccant wheel is first to reduce the humidity of outside air in order to match

indoor air standards and second to provide an extra dehumidification to increase the potential of

supply humidifier. The desiccant wheel appears as a key component. The dehumidification

performance of the desiccant wheel depends on the operating conditions [1] e.g. the wheel rotation

speed, the air flow rate, the outside temperature and outside humidity, the regeneration temperature

and regeneration humidity. Usually an optimum rotation speed and optimum air flow rate are

recommended by the manufacturer thus these two parameters are constant during the operations

but outside and regeneration conditions are not. So the performance of the desiccant wheel depends

intrinsically on these parameters.

In this paper a sensitivity analysis is conducted on a desiccant wheel using the silica gel as anadsorbent to investigate the effect of outside and regeneration conditions on the performance of the

desiccant wheel. The method used in this analysis is design of experiments (DOE) [2]

2. Sensitivity analysis

2.1. Design of experiments

In the DOE the response (y) of the studied phenomena influenced by different parameters or

factors (xi) is expressed using a polynomial form [2]:

NiN

N

kji

kjiijk

N

ji

jiij

N

i

ii xxaxxxaxxaxaay ...... ...11,1,11,11

0 +++++= ======

(1)

y is the response of the phenomenaxi is a factor or parameter influencing the phenomenaa0 is a constant effect,ai is the effect of single parameteraij is the effect of double interaction,aijk is the effect of triple interactionIt is evident that the number of effect to be determined will need the same number of experiments.

In order to estimate the effects, each parameter varies between an upper and lower limit, so each

parameter has two levels [2]. In our case we have 4 parameters; each one varying between 2 limits

which mean we have 2

4

effects to be determined and 16 combinations (experiments) are thenneeded.

The following range of the parameters was considered:Outside temperature T1: [25, 35] [C]Outside humidity ratio w1: [11, 14.5] [g/kg]Regeneration temperature T8 [55, 75] [C]Regeneration humidity ratio w8 [10; 15] [g/kg]Outside temperature and humidity ranges correspond to the most of the European climates (except

some humid Mediterranean climates) and match with the domain of application of desiccant

cooling (e.g. moderately hot and moderately humid climates). The upper limit of regeneration

temperature domain is consistent with solar application with temperature not exceeding 75C while


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the lower limit is the minimum required for the silica gel. For the regeneration humidity ratio range

it is taken with the consideration of the outlet conditions of the return humidifier.

2.2. Experimental setup

The experimental installation of La Rochelle [1] is used for the measurements of the performanceof the desiccant wheel. This experimental installation consists of a silica gel desiccant wheel and

aluminum sensible regenerator and two rotating humidifiers. At the inlet and outlet of each

component a psychrometer is used to measure the dry and wet bulb temperature. The local

atmospheric pressure is measured too thus using the dry and wet blub temperature the humidity

ratio is then measured accurately. At the desiccant wheel outlet, the dry bulb temperature and the

humidity ratio are not uniform. In order to have an accurate measurement of the mean outlet

temperature and humidity, three humidity measurements and 6 temperature measurements are

performed simultaneously.

The major parts of the dehumidification rates (w1-w2) used in the sensitivity analyses are

experimental measurements but when a combination of parameters is not possible experimentallynumerical results of the desiccant wheel model are used to complete the required combinations.

The model used will be introduced in the following section.

3. Desiccant wheel model

3.1. Model description

The heat and mass transfer model for the desiccant wheel used below is based on the analogy

method with heat transfer that occurs in the sensible heat regenerator. It was first introduced by

Banks [3] and Maclaine cross [4] then Jurinak [5] and Stabat [6] improved the model. The

following assumptions are considered:

The state properties of the air streams are spatially uniform at the desiccant wheel inletThe interstices of the porous medium are straight and parallelNo leakage or carry-over of streamsThe interstitial air velocity and pressure are constantHeat and mass transfer between air and porous desiccant matrix is considered using lumpedtransfer coefficients

Diffusion and dispersion in the fluid flow direction are neglectedNo radial variation of the fluid or matrix statesThe sorption isotherm does not represent a hysteresisAir reaches equilibrium with the porous mediumThe heat and mass conservation equations:

0=

+

+

t

H

z

hu

t

h daa

(2)

0=

+

+

t

W

z

wu

t

w daa (3)


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Heat and mass transfer equations:

0)())(( ,, =

+

+

Ta

aaeqa

wa

aaeqam

d

w

hww

T

hTTLeJ

t

H

(4)

0)( , =+

aeqam

d wwJt

W

(5)

Equations (2), (3), (4) and (5) are coupled hyperbolic non-linear. With the assumption of the Lewis

number(Le), equal unity and the desiccant matrix in equilibrium with air means (Td= Teq andweq=

wa). Banks [2] used matrix algebra and proved that these equations can be reduced using potential

functionFi(T,w) to the following system:

0,,,

=

+

+

z

F

t

Fut

Faiai

eqi

i i=1;2

(6)

0)( ,,, =+

aieqim

di

i FFJt

F i=1;2

(7)

Introducing the equations of heat transfer alone in the sensible regenerator as stated in [3]:

0=

++

+

t

Tm

cwc

c

z

Tau

t

Ta

pvapa

pm

(8)

0)( , =+

+amat

pvapa

pmTTJ

t

Tm

cwc

c

(9)

These equations (6) and (7) are similar to those of the sensible regenerator (8) and (9). In the case

of the desiccant wheel the potential function Fi replace the temperature and the parameters i

replace the specific heat ratio. Thus these equations can now be solved using analogy with heat

transfer alone [3] by applying the correlation introduced by Kays [7] for the sensible regenerators

given by:

( )

=93.1*9

1

1r

cfC

(10)

Where

min

*..

C

NcMC

pmm

r =

(11)

cf

cf

cfNUT

NUT

+=

1

(12)

cfis the efficiency of the counter flow heat exchanger for balanced flow.


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Many expressions exist for the potential functions of silica gel - air; we chose those used [6].

hF =1 (13)

( ) 8.05.12 1.1

6360

15.273 wTF ++=

(14)The model described above, was implemented to SPARK [8] a general simulation environment

based on equation. In the next section the model is validated experimentally.

3.2. Experimental validation

The experimental installation presented in section 2 is used to validate the above presented model.

Different inlet conditions were considered with temperature varying form 25C to 38C and

humidity ratio from 10 to 15 g/kg and for different regeneration temperature (55C, 60C 65C,

70C and 80C).

-3

-2.5

-2-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-1 -0.75-0.5-0.25 0 0.25 0.5 0.75 1

Te

mperature

error

(

C)

Humidity ratio error (g/kg)

Desiccant wheel

Treg=80Treg=70

Treg=65

Treg=60

Fig. 2. Temperature error versus humidity ratio error at the outlet of the desiccant wheel

The figure 2 [9] plots the temperature error versus the humidity ratio error for the most significant

points. It shows the maximum predicted error 0.4 g/kg and root mean squared error (RMSE) is

0.22 g/kg. For the temperature and the maximum committed error in the outlet temperature is 1 C

for RMSE of 0.65 C. It must be noted that the uncertainty in the measurement of the mean valuesis 0.7C for the temperature and 0.3 g/kg. It shows that the committed errors are in the domain of

the uncertainty of the measurements.

In the following section the experiments are performed on the desiccant using experimental

measurements and numerical results in order to perform the sensitivity analsysis.

4. Sensitivity results and analysis

4.1 Results

Experiments have been conducted on the desiccant wheel with the parameters (e.g. outside

temperature, outside humidity ratio, regeneration temperature and regeneration humidity ratio)

varying in the range defined in the section 2. The complete DOE of 4 parameters operating

between 2 levels needs 24=16 experiments. When a combination of the studied parameters was


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difficult to achieve experimentally (3 experiments) the results of the model was used to complete

the DOE. Table 1 below shows the results

Table 1. Dehumidification rate of the desiccant wheel for different operating conditions

T1 w1 T8 w8 w1-w2 T1 w1 T8 w8 w1-w2[C] [g/kg] [C] [g/kg] [g/kg] [C] [g/kg] [C] [g/kg] [g/kg]25 11 55 10 4.8 35 11 55 10 2.9

25 11 55 15 3.6 35 11 55 15 1.7*

25 11 75 10 6.8 35 11 75 10 5.2

25 11 75 15 5.8 35 11 75 15 4.1

25 14.5 55 10 5.4* 35 14.5 55 10 4.1

25 14.5 55 15 4.3 35 14.5 55 15 2.95

25 14.5 75 10 8 35 14.5 75 10 6.7

25 14.5 75 15 7 35 14.5 75 15 5.6*

* Calculated by the model

Solving 16 equations for the effects identified in the equation (1). The dehumidification of thedesiccant wheel is then written in function of the operating parameters

5

)5,12(

20

)65(053,0

5

)5,12(

4

)75.12(0788,0

20

)65(

4

)75.12(0563,0

5

)5,12(

10

)30(086,0

20

)65(

10

)30(0888,0

4

)75.12(

10

)30(0425,0

5

)5,12(491,0

20

)65(1438,1

4

)75.12(6275,0

10

)30(828,0987,4

888181

818111

881121

+

+

+

+

+

+

=

wTwwTw

wTTTwT

wTwTww

The equation was limited to the double effect (negligible indeed) since for the triple effect and

above effects are very close to zero.

4.2 Analysis

Form the equation identified we notice a constant dehumidifying effect of 4,987 g/kg which will be

increased or decreased depending on the operating conditions. In order to compare the effect of

each parameter with the constant effect, they are divided by this later and a graphical comparison

can thus be established. The figure below shows the effect of each parameter.

As commonly known, figure 3 shows tha the regeneration temperature has the most significant

impact on the dehumidification performance of the desiccant wheel. In the same time outside

conditions has an important impact on too.

Increasing the regeneration temperature from the mean value (65C) to its upper limit willincrease the dehumidification 23%Increasing the outside temperature to its higher limit will decrease the dehumidification of 17%.Increasing the outside humidity ratio will increase the performance of the desiccant wheel of 13%Increasing the regeneration humidity ratio will decrease the performance of the desiccant wheelof 8%.

The reason behind these observations is the vapor pressure difference of the air and that of thesurface of the silica gel. This vapor pressure difference is the driving force of the adsorption

phenomena. Reminding that if the desiccant is cold the vapor pressure at its surface. For the moistair the temperature does not have a significant impact on the vapor pressure while humidity ratiodoes.


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The desiccant coming for the regeneration sector is hot and dry, it is first cooled down by the

outside air in the process sector and then the adsorption occurs.

-30

-20

-10

0

10

20

30

T

1

w

1

T

8

w

8

T

1.w1

T

1.T8

T

1.w8

w

1.T8

w

1.w8

T

8.w8

Effect

of

the

parameter

[%]

Parameter

Fig. 3 Effect of the operating conditions and their combinations

So if we increase the temperature of the outside air its vapor pressure will not increase significantly

in reversal it will not cool sufficiently the hot desiccant form arriving from the regeneration sector

yielding a high vapor pressure at the surface of the desiccant and thus the adsorption will be less

efficient. If we increase the humidity ratio of the outside air its vapor pressure will increase

significantly yielding a higher vapor pressure difference thus increasing the adsorption. When

increasing the regeneration temperature, the regeneration air vapor pressure does not increase

significantly while the desiccant is heated and its vapor pressure increases leading to an efficientdrying of the desiccant. This desiccant leaving the regeneration sector is dry and thus having fewer

vapor particles, yielding a low vapor pressure at its surface and thus high adsorption. When

increasing the regeneration humidity ratio we will increase the vapor pressure of regeneration air

stream, reducing the transfer from the desiccant to the regeneration air, yielding less drying of the

desiccant. When the sorbent will leave the regeneration with more water vapor at its surface its

vapor pressure is then higher, reducing thus the adsorption.

This clearly shows the limitations of the desiccant cooling technique regarding outside conditions.

It demonstrates that high outside temperature reduces significantly the performance of the

desiccant wheel. Regarding the outside humidity ratio even if the dehumidification increase with

increasing outside humidity ratio, we noticed that for outside temperature beyond 30C the

maximum dehumidification rate is 6 g/kg. Taking into account the maximum humidity inside the

building (e.g. 11.8 g/kg) and the humidification across the supply humidifier we conclude that the

maximum outside humidity under which a desiccant system will operate efficiently is 14.5 g/kg.

5. Conclusion

In this paper a sensitivity analysis based on the design of experiments was conducted on a

desiccant wheel using mainly experimental results. A numerical model was validated

experimentally and provided the missing combination of the experiments. The impact of the

outside and regeneration conditions on the dehumidification rate of the desiccant wheel was

studied. As widely known the regeneration temperature has the most significant impact on the

dehumidification rate, but the impact of the outside temperature, outside humidity ratio and the


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regeneration humidity ratio are very important as well. These results showed that desiccant cooling

is an interesting option for moderately hot and moderately humid climates

Nomenclature

cpa heat capacity of air [J.Kg-1

.K-1

]

cpv heat capacity of water vapour

[J.Kg-1

.K-1

]

cpm heat capacity of the regenerator matrix

[J.Kg-1

.K-1

]

C heat capacity (J.Kg-1

.K-1

)

Fi potential characteristic [-]

ha enthalpy of moist air [J.Kg-1

]

H enthalpy of the desiccant [J.Kg-1

]

Jt lumped heat transfer coefficient [s-1]Jm lumped mass transfer coefficient [s

-1]

Le Lewis number [-]

ma air mass flow rate [Kg.s-1

]

Md mass of the desiccant matrix [Kg]

Mm mass of the aluminium matrix [Kg]

N angular speed of the wheel [rd.s-1

]

NUT number of transfer unit [-]

RMSE Root mean squared error

[unity of the variable]

t time [s]

T temperature [K]

Ta air temperature [K]

Teq equilibrium temperature [K]

Tm matrix temperature [K]

u fluid velocity (m.s-1

)

wa humidity ratio of moist air. [Kg/Kg]Wd water content of desiccant [Kg/Kg]

z coordinate in the flow direction [m]

ratio of matrix mass over air mass [-]

efficiency [-]

density [Kg.m-3

]

i parameter [-]

Acknowledgments

The authors would like to thank Mr Michel Burlot for his valuable technical support on the experimental

installation. This work was supported by ADEME (French Agency of the Environment and EnergyManagement) and the regional council of Poitou Charentes.

References

[1] P. Bourdoukan., E. Wurtz., P. Joubert., M. Sperandio,. (2008). Potential of solar heat pipe vacuum

collectors in the desiccant cooling process: modelling and experimental results. Solar Energy.

0.1016/j.solener.2008.06.003

[2] J. Goupy, (2001). Introduction aux plans d'expriences, Dunod.

[3] P.J. Banks, (1972). Coupled equilibrium heat and single adsorbate transfer in field flow through a porous

medium- 1. Caracteristics potentials and specific capacity ratios. Chemical Engineering Science, 27,

1143-1155.

[4] I.L. Maclaine-cross, P.J. Banks, (1972). Coupled heat and mass transfer in regenerators- prediction using

analogy with heat transfer. Int. J. Heat Mass Transfer, 15, 1225-1242.

[5] J.J. Jurinak. (1982). Open cycle solid dessicant cooling - component models and system simulation, Ph.D,

Winconsin, Madison.

[6] P. Stabat, (2003). Modlisation de composants de systmes de climatisation mettant en oeuvre

l'adsorption et l'evaporation d'eau, Ph.D, Ecole des Mines, Paris.

[7] W.M. Kays, A.L London, (1984). Compact Heat Exchangers, McGraw-Hill, New York.

[8] SPARK. (2003). Simulation Problem Analysis and Research Kernel. LBNL, Berkeley,California.

[9] P. Bourdoukan., E. Wurtz., P. Joubert., M. Sperandio, (2008). Critical efficiencies of components in

desiccant cooling cycles and a comparison between the conventional mode and the recirculation mode."In proceedings of ECOS conference, Krakow, Poland, 1, 435-443

a sensitivity analysis of a desiccant wheel

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