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Effectiveness of desiccant coated regenerative wheels from transient response characteristics and flow channel properties--Part II: predicting and comparing the latent effectiveness of dehumidifier and energy wheels using transient data and properties.

Article Excerpt
INTRODUCTION

Shang and Besant (2009) presented a theoretical frame work for the prediction of latent energy or moisture transfer effectiveness of desiccant coated wheels. This companion to that paper presents the factors that will cause changes to the moisture transfer characteristics of desiccant coated wheels and compares transient moisture transfer characteristics to equilibrium moisture content isotherms. This paper shows that a new characteristic moisture transfer time constant is needed to predict the behavior of typical dehumidifier and energy wheels.

TEMPERATURE EFFECTS DUE TO SORPTION

The moisture adsorption or desorption on desiccant coatings causes a temperature rise or fall in both the matrix and the outlet air flowing due to the phase change of water vapor. For a transient step change in inlet humidity, the temperature rise (or fall) of the outlet air due to moisture adsorption (or desorption) can be measured while the inlet temperature is held constant. It will be shown that these transient temperature measurements may be a more accurate method to determine the characteristic moisture sorption time constant and the moisture or latent effectiveness of a typical dehumidifier or energy wheels. These effectiveness predictions are compared with measured steady-state data for energy wheels.

Figure 1 shows a schematic of the test setup for the transient humidity step-change response for a parallel flow step change as described by Wang et al. (2005). For this test, the two inlet flows have the same temperature but different relative humidities. Figure 2 shows the outlet humidity response, [W.sub.o], due to a step change in the inlet humidity, [W.sub.i], for (a) molecular sieve and (b) silica gel coatings on similar 100 mm thick wheels using data from Wang (2005).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The data in Figure 2 shows that the transient water vapor transfer process is evident for times much larger than the duration of a typical step for energy wheels, and the desorption process is different than the adsorption process.

Figure 3 shows the inlet and outlet air temperatures for the same moisture adsorption and desorption processes shown in Figure 2 for (a) molecular sieve desiccant coating and (b) silica gel desiccant coating on two energy wheels.

[FIGURE 3 OMITTED]

These airflow processes, with large steps in humidity at the inlet while the inlet air temperature remains constant, result in large sorption effects and energy changes due to phase change accompanied by small but significant temperature changes and coupled heat transfer effects. The transient sorption of water vapor is best modelled by Equation 1 for continuity of water. For heat transfer, Equation 7 in Shang and Besant (2009) is modified by adding a heat source term to account for the heat of water vapor sorption, which gives the following:

[[tau].sub.S][[d[THETA]]/dt] + [THETA] = [+ or -][e.sup.-t*] (1)

where the plus sign is for adsorption and the negative sign is for desorption in the flow channel coating; t* is the dimensionless time, t* = t/[[tau]*.sub.w];

[THETA] = [([T.sub.o] - [T.sub.i])/[DELTA][T.sub.w]] (2)

is a dimensionless temperature due to sorption;

[DELTA][T.sub.w] = [[[h.sub.ad][DELTA][W.sub.M]]/[c.sub.pa]] (3)

is a characteristic maximum temperature difference due to phase change humidity ratio step size, [DELTA][W.sub.M]; and [h.sub.ad] is the heat of sorption during this phase change.

The solution of Equation 1with a transient heat source term due to the phase change of water for the initial condition is [THETA](t = 0) = is

[THETA] = [+ or -][absolute value of [e.sup.-t'] - [e.sup.-t*]], (4)

where the plus sign is taken for moisture adsorption by the coating, the negative sign is for moisture desorption, and t' = t/[[tau].sub.s] is the dimensionless time. This equation also satisfies the final physical condition that the temperature of the outlet air, after a long time, returns to the inlet temperature--i.e.,[THETA](t [right arrow] [infinity]) = 0. In this solution, [[tau].sub.s] can be either greater than [[tau]*.sub.w], as it appears to be for this molecular sieve matrix coating, or less than [[tau]*.sub.w], as it appears to be for the silica gel coating.

The theoretical maximum value of [THETA] occurs when the time after the step change is

t([THETA] = [[THETA].sub.m]) = ln[([[tau].sub.S]/[tau]*.sub.w])/([1/[tau]*.sub.w]] - [1/[[tau].sub.S]])], (5)

where is [[THETA].sub.m] either the maximum or minimum value of [THETA]. When Equation 5 is substituted into Equation 4, we get the equation for [[THETA].sub.m]. A first order approximation of [[THETA].sub.m] results in the very simple equation

[[THETA].sub.m] = [+ or -][absolute value of (y/2)], (6)

where y=[[tau].sub.s]/[[tau]*.sub.w]-1.

Equation 6 is not expected to be valid when [[THETA].sub.m] is much larger than 0.2. For example, for a theoretical value of [[tau].sub.s] = 13.3s and [[THETA].sub.m] = 0.13[[tau]*.sub.w], would have a value of 10.5 s for a molecular sieve coating and [[tau]*.sub.w] = 13.3 s for the silica gel coatings. Equation 6 shows that as [absolute value of ([[THETA].sub.m])] or [absolute value of (y/2)] decreases, [[tau]*.sub.w] approaches [[tau].sub.s] either from a lower value of [[tau]*.sub.w], as for the molecular sieve coating, or a higher value of [[tau]*.sub.w], as for the silica gel coating. For the special cases of a coating when [[THETA].sub.m] = 0, it implies [[tau]*.sub.w] = [[tau].sub.s], and when [[THETA].sub.m] [right arrow] [infinity], it implies [[tau]*.sub.w] [right arrow] 0.

This simple method to determine [[tau]*.sub.w] from temperature measurement data when the desiccant coated energy wheel is subjected to a large step change in the inlet air humidity ratio is expected to avoid the problems with humidity sensor transient characteristics and the two weighted time constants that result from correlating the data over 1000 s or more. The maximum temperature, [absolute value of([[THETA].sub.m])], always occurs when

t([THETA] = [[THETA].sub.m]) [congruent to] [1/2]([[tau].sub.s] - [tau]*.sub.w]),

which emphasizes the importance of the data within about 10 to 15 s of the step change for the data shown above and avoids curve fitting correlations over extended time periods. Energy wheels, which cycle from inlet supply to exhaust air and back every second or two, do not need long-term data, and dehumidifier wheels cycle between the regenerator and the supply every 20 to 60 s or so. Table 1 summarizes the data for the two energy wheels tested.

Table 1. Characteristic Data for the Molecular Sieve and Silica Gel Coated Energy Wheels Presented in Tables 1 and 3 in Shang and Besant (2009) Wheel [[tau].sub.s], Sorption [absolute value of [[tau]*.sub.w] Matrix s ([[THETA].sub.m])] Coating MS 13.3 Adsorption 0.123 10.7 Desorption 0.107 11.0 SG 10.7 Adsorption 0.121 13.3 Desorption 0.105 12.9 Wheel [[beta].sub.dc] [[beta].sub.p] [X.sub.dc] [X.sub.p] Matrix Coating MS 2.02 0.273 0.416 0.584...

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