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Run-around energy recovery system for air-to-air applications using cross-Flow exchangers coupled with a porous solid desiccant--part II: results and performance sensitivity.

INTRODUCTION

Because it is the most common way of providing good indoor air quality, ventilation of buildings is extremely important (Wargocki and Wyon 2007a, 2007b; Russell et al. 2007; Melikov and Knudsen 2007; Kaczmarczyk et al. 2006), and air-to-air energy exchangers are widely used to transfer heat and moisture between exhaust and supply airflows for buildings because they reduce energy consumption and heating and cooling equipment capacities and are often the least costly design alternative (Fauchoux et al. 2007; Asiedu et al. 2004; Simonson 2007). Desiccant-coated energy wheels are the most common exchangers used in buildings because they transfer both heat and moisture, have high effectiveness values, and are low in cost (Freund et al. 2003; Simonson and Besant 1999a, 1999b). However, there are some inherent disadvantages of regenerative energy wheels, and as a result they cannot be used cost effectively for all possible HVAC applications, especially when retrofitting existing buildings where the supply and exhaust ducts are not side by side. The run-around system investigated for this paper permits heat and moisture transfer between remote supply and exhaust air streams using a moving porous bed and therefore has the potential to have a large impact in the retrofit market because the supply and exhaust ducts do not need to be side by side.

The governing equations for heat and moisture transfer in the novel run-around system that uses a solid material to transport heat and moisture between remote air streams are listed in Part I (Li et al. 2009). The run-around energy recovery system is shown in Figure 1, which is the same as Figure 1 in Part I. In Part I, the accuracy of the model was verified for the heat and moisture transfer in the run-around system by comparing it to effectiveness correlations in the literature. In this part, moisture transfer coupled with heat transfer in the run-around system is investigated.

[FIGURE 1 OMITTED]

THE RESULTS FOR A RUN-AROUND SYSTEM WITH HEAT TRANSFER ONLY

For the run-around system with heat transfer only, Figure 2 shows the sensitivity of the overall effectiveness to changes in Cr (Cr = [C.sub.min]/[C.sub.max]) and number of transfer units (NTU). For [C.sub.s] < [C.sub.g] and a constant NTU, the effectiveness decreases as Cr decreases. For [C.sub.s] > [C.sub.g], where NTU is constant (i.e., a constant air velocity) and NTU < 3, the overall effectiveness remains almost constant and independent of the velocity of the porous bed. When NTU > 3, the effectiveness decreases as Cr decreases, which means the effectiveness decreases as the velocity of the porous bed increases. At a constant NTU and NTU > 1, the maximum effectiveness occurs at Cr [approximately equal to] 1.

[FIGURE 2 OMITTED]

In order to obtain the maximum effectiveness during peak load conditions, [C.sub.s]/[C.sub.g] should be kept between 0.9 and 1.2. For example, when 0.9 [less than or equal to][C.sub.s]/[C.sub.g][less than or equal to] 1.2 and NTU = 5, the overall sensible effectiveness of the run-around system will be almost 60%. With the same [C.sub.s]/[C.sub.g] and NTU = 10, the overall sensible effectiveness can be almost 70%. During the part-load conditions, the overall effectiveness can be reduced to match the load by reducing [C.sub.s], which can be fulfilled physically by reducing the velocity of the porous bed.

SINGLE EXCHANGER WITH HEAT AND MOISTURE TRANSFER

In each exchanger, the porous bed's properties are shown in Table 1, as they are in Part I (Li et al. 2009). The operating conditions for one exchanger are chosen, as in Table 2. These inlet properties will be used to illustrate the behavior of one exchanger during two somewhat extreme operating conditions (i.e., one warm and moist and the other warm and dry) in summer for the solid desiccant. It is important to note that the purpose of this section is not to demonstrate the performance of a desiccant drying system including the energy required to regenerate the desiccant but to demonstrate the heat and moisture transfer characteristics of a moving porous bed exchanger and demonstrate the reliability of the numerical model. In subsequent sections (sections 5 and 6), regeneration of the desiccant will be considered where, for example, during hot and humid weather, the desiccant will be shown to absorb moisture from the supply airstream and be passively regenerated by the exhaust airstream. There is no need for external regeneration energy when the run-around system is operated in this way. Investigation of the run-around system with an external heat source for regeneration of the desiccant in drying applications or contaminant removal is left for other studies (Wolfrum et al. 2008; Tsay et al. 2006).
Table 1. Parameters and Properties of Each Heat and Moisture Exchanger

Size of the Exchanger       [X.sub.0] x [Y.sub.0]  0.3 x 0.3 x 0.3 m
                                 x [Z.sub.0]         (1 x 1 x 1 ft)

Fiberglass Volume Fraction    [[epsilon].sub.f]          0.1%

Silica Gel Volume Fraction    [[epsilon].sub.si]         0.5%

Table 2. Selected Operating Conditions of Each Heat and Moisture
Exchanger

Inlet Temperature of          35[degrees]C            35[degrees]C
the Airstream                (95[degrees]F)          (95[degrees]F)

Inlet Relative Humidity          47.4%                   47.4%
of the Airstream

Inlet Humidity Ratio of    16.90 g/kg (0.0169      16.90 g/kg (0.0169
the Airstream            [lb.sub.m]/[lb.sub.m])  [lb.sub.m]/[lb.sub.m])

Inlet Temperature of         23.9[degrees]C          23.9[degrees]C
the Solid Stream             (75[degrees]F)          (75[degrees]F)

Inlet Equilibrium                51.2%                     25%
Relative Humidity of
the Solid Stream

Inlet Equilibrium          9.51 g/kg (0.0095       4.61 g/kg (0.0046
Humidity Ratio of the    [lb.sub.m]/[lb.sub.m])  [lb.sub.m]/[lb.sub.m])
Solid Stream


As in Part I (Li et al. 2009), the numerical results are calculated with space step [DELTA]x = [DELTA]y = 6 mm, so the number of nodes m and n = 1 to 51. The temperature and humidity ratio distributions for moist solid inlet operating conditions ([T.sub.g,in] = 35[degrees]C or 95[degrees]F, [[phi].sub.g,in] = 47.4%, [T.sub.sl,in] = 23.9[degrees]C or 75[degrees]F, [[phi].sub.sl,in] = 51.2%-listed in Table 2) with NTU = 6 and Cr = 1 are presented in Figure 3. Inside the exchanger, the air temperature and humidity ratio are higher than those of the solid, and the heat and moisture are transferred from the air to the solid. As the solid desiccant moves through the exchanger f (from top to bottom in Figure 3), it adsorbs moisture from the moist air and the heat of adsorption is delivered to the solid. The temperature and moisture content gradients are large (close contour lines in Figure 3) near the inlet of the solid (Y* = 0) because the heat and moisture transfer rates between the hot and humid air and the cold and dry desiccant are very large. As the solid desiccant gains heat and moisture, the heat and moisture transfer rates between the air and the desiccant decrease and the temperature and humidity ratio contour lines move farther apart. The lower-left half of the exchanger is nearly void of contour lines, indicating that the capacity rate of the solid should be increased so that the heat and moisture transfer will occur throughout the entire exchanger. Since the temperature and moisture content of the solid are nearly constant (due to low heat and moisture transfer rates) in the lower left corner of the exchanger, the temperature and humidity ratio gradients in the air are mainly in the airflow direction (i.e., the x--direction) in this region. As a result, the temperature and humidity ratio contours in Figures 3a and 3c are nearly vertical near the air inlet (X* = 0) and are diagonal near the air outlet (X* = 1). The bulk air humidity ratio is lower at the outlet than at the inlet, and the bulk solid equilibrium humidity ratio is higher at the outlet than at the inlet. Moisture is transferred from the air to the solid for most of the exchanger, but in the bottom-left corner (X* full range, Y* large), moisture is transferred from the solid to air because the humidity ratio (vapor density) of the solid is higher than that of the adjacent moist air. The actual amount of this "reverse" moisture transfer, however, is quite small under the selected operating conditions but would be higher if the temperature of the solid entering the exchanger was increased.

[FIGURE 3 OMITTED]

In Figure 4, the temperature and humidity ratio distributions for the case where the solid entering the exchanger is dry ([T.sub.g,in] = 35[degrees]C or 95[degrees]F, [[phi].sub.g,in] = 47.4%, [T.sub.sl,in] = 23.9[degrees]C or 75[degrees]F, [[phi].sub.sl,in] = 25% with NTU = 6, and Cr = 1) are presented. Here only [[phi].sub.sl,in] is different compared with the operating conditions shown in Figure 3. During this operating condition, the temperature distribution shows that the air temperature in the bottom-left region (X* full range, Y* large) is higher than the temperature of the air entering the exchanger. In this region, the solid temperature is higher than that of air. The bulk temperature of the air at the outlet is higher than that of the air at the inlet, even though the temperature of the solid at the inlet is lower than the temperature of the air at the inlet. This occurs because a large amount of adsorbed water accumulates on the desiccant surface due to the large relative humidity (vapor density) difference between the air and solid. As water is adsorbed, the heat of sorption is delivered to the solid and this sorption heat release is large enough to make the solid temperature higher than that of the adjacent air. Similar phenomena are observed in desiccant drying applications.

[FIGURE 4 OMITTED]

Figure 5 and Figure 6 are used to illustrate the effect of changing the ratio Cr. In Figures 5 and 6, the temperature and humidity ratio distribution are presented for the moist operating condition in Table 2 with NTU = 6 and Cr = 0.3. The results in Figure 5 (for [C.sub.sl] < [C.sub.g]) and the results in Figure 6 (for [C.sub.sl] > [C.sub.g]) are presented. Figure 5 shows that there are only small temperature and humidity ratio differences between inlet and outlet for the air side but that large temperature and humidity ratio differences between inlet and outlet exist for the solid side. This is expected because the capacity rate of the solid is much lower than that of the air.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Figure 6 shows that there are large temperature and humidity ratio differences between the inlet and outlet on both the air and solid sides. The temperature and humidity ratio contours are nearly uniformly spaced throughout the entire exchanger, which indicates that there is significant heat and moisture transfer throughout the entire exchanger and no "dead" areas with little or no heat/moisture transfer. The temperature and humidity ratio distributions in Figure 6 have a similar shape to those presented in Part I (Li et al. 2009) for sensible heat transfer in a single heat exchanger with [C.sub.sl] = [C.sub.g] (Cr = 1). Since Cr = 1 is the optimal capacity ratio for sensible exchangers coupled in a run-around system, this may indicate that the optimal capacity ratio for a run-around heat and moisture exchanger system composed of two heat and moisture exchangers (see section "Run-Around Exchange with Heat Transfer and Moisture Transfer") is Cr = 0.3 with [C.sub.sl] > [C.sub.g]. This is consistent with the results of Fan et al. (2006). The temperature and humidity ratio contours in Figure 6 are quite different from those in Figure 5, even though they have the same heat capacity ratio.

EFFECTIVENESS OF A SINGLE EXCHANGER WITH HEAT AND MOISTURE TRANSFER

For a single exchanger, the sensible effectiveness and latent effectiveness with ARI (2005) summer operating conditions ([T.sub.g,in] = 35[degrees]C or 95[degrees]F, [[phi].sub.g,in] = 47.4%, [T.sub.sl,in] = 23.9[degrees]C or 75[degrees]F, [[phi].sub.sl,in] = 51.2%) are presented in Figure 7. For a single exchanger with the same NTU and Cr, the sensible and latent effectivenesses for [C.sub.sl] > [C.sub.g] are larger than those for [C.sub.sl] < [C.sub.g].

[FIGURE 7 OMITTED]

In Figure 7a, the sensible effectiveness is minimum when the heat capacity ratio is Cr = 1. As Cr decreases (i.e., as [C.sub.sl]/[C.sub.g] increases for [C.sub.sl]/[C.sub.g] > 1 and [C.sub.sl]/[C.sub.g] decreases for [C.sub.sl]/[C.sub.g] < 1), [[epsilon].sub.s] increases. This result is similar to that for sensible heat exchangers (Kays and London 1984; Fan et al. 2005; Li et al. 2009; Li 2008). In Figure 7b, the latent effectiveness increases as [C.sub.sl]/[C.sub.g] increases over the full range of [C.sub.sl]/[C.sub.g]. This trend is consistent with the results of Fan et al. (2006) for liquid desiccant-to-air exchangers but different from the results for sensible heat exchangers. An explanation for the different trends in the sensible and latent effectivenesses is as follows: it is logical that as the velocity of the moving solid goes to zero (i.e., [C.sub.s][right arrow]0), the outlet air temperature and humidity ratio will approach the inlet air temperature and humidity ratio (i.e., both the heat and moisture transfer rates will approach zero). Therefore, in the effectiveness equation, both the numerator (heat or moisture transfer rates) and the denominator (the minimum heat or moisture capacity rate) approach zero. The fact that the latent effectiveness approaches zero means that the moisture transfer rate approaches zero more quickly than the moisture capacity rate. Conversely, as [C.sub.sl]/[C.sub.g] decreases below 1, the heat transfer rate decreases more slowly than the heat capacity rate, resulting in an increase in sensible effectiveness. These trends are likely to differ for different operating conditions when the heat and moisture change directions and magnitudes change significantly; similarly, the part-load performance of energy wheels was found by Simonson et al. (2000a, 2000b) to depend on the operating condition factor.

RUN-AROUND EXCHANGER WITH HEAT TRANSFER AND MOISTURE TRANSFER

The run-around heat and moisture recovery system has separate exchangers in the supply and exhaust airstreams. The scheme for the run-around system is shown in Figure 1. ARI summer and winter test conditions (ARI 2005) shown in Table 3 are used for the simulation where each exchanger has the properties listed in Table 1.
Table 3. ARI Standard 1060 (ARI 2005) Inlet Air Certification Test
Conditions

                              Summer          Winter

Inlet Temperature of the   35[degrees]C   1.7[degrees]C
Supply Airstream          (95[degrees]F)  (35[degrees]F)

Inlet Relative Humidity       47.4%           82.5%
of the Supply Airstream

Inlet Temperature of the  23.9[degrees]C  21.1[degrees]C
Exhaust Airstream         (95[degrees]F)  (70[degrees]F)

Inlet Relative Humidity       51.2%           49.2%
of the Exhaust Airstream


Figure 8 shows the sensible, latent, and total effectivenesses of the run-around system with NTU as a parameter during ARI (2005) summer operating conditions. For NTU [greater than or equal to] 5.0, the peak sensible, latent, and total effectivenesses occur when the heat capacity ratio Cr = 0.3 ([C.sub.sl]/[C.sub.g] = 3.3). That is, the heat capacity rate of the solid is about 3.3 times larger than the moist air. For NTU < 5.0, these effectivenesses are somewhat insensitive to [C.sub.sl]/[C.sub.g] for [C.sub.sl]/[C.sub.g] > 3.0. These results are very close to the results of Fan et al. (2006), especially for the sensible effectivenesses, which are almost identical. This comparison further verifies the model with moisture and heat transfer.

Figure 8 shows that all three effectiveness values decrease as [C.sub.sl]/[C.sub.g] decreases below 3.3 for the run-around system. This means that during part-load operating conditions of the HVAC system (Simonson et al. 2000a, 2000b), the heat and moisture transfer rates can be controlled by controlling the flow rate of the coupling solid. For maximum performance, the flow rate of the solid desiccant should be set so that its heat capacity rate is 3.3 times the heat capacity rate of the airflow. The optimal value of 3.3 may change slightly when the air pressures drop across the exchangers and the energy required to transport the coupling solid (which are neglected in this study) are included.

It is interesting to note that the sensible effectiveness of the run-around system decreases as [C.sub.sl]/[C.sub.g] decreases below 3.3 in Figure 8, while the sensible effectiveness of a single exchanger increases as [C.sub.sl]/[C.sub.g] decreases below 1 in Figure 7. This is because the heat capacity rate of the coupling solid does not appear in the effectiveness definition for a run-around system, though it is in the denominator of the effectiveness equation for a single exchanger (Li et al. 2009). As the heat capacity rate of the solid decreases ([C.sub.sl]/[C.sub.g] below 1 for a single exchanger and [C.sub.sl]/[C.sub.g] below 3.3 for a run-around system), the total heat transfer rate between the solid and the airstream (i.e., the numerator in both effectiveness definitions) decreases for both the single exchanger and the run-around system. At the same time, the denominator in the effectiveness equation remains constant for the run-around system and decreases for the single exchanger. The result is that as the heat capacity rate of the solid decreases, the effectiveness of the run-around system decreases, while the effectiveness of the single exchanger increases even though the heat transfer rates decrease in both systems.

Figure 9 shows the sensible, latent, and total effectivenesses of the run-around system with NTU as a parameter during ARI (2005) winter operating conditions. For this winter condition and NTU [greater than or equal to] 5.0, the peak sensible, latent, and total effectivenesses occur when the heat capacity ratio is Cr = 0.5 ([C.sub.sl]/[C.sub.g] = 2); i.e., when the heat capacity rate of the solid is about twice that of the moist air.

For the run-around system with only heat transfer, and using dry air with the same operating temperature as in summer ARI (2005) operating conditions, the results were illustrated in Part I (Li et al. 2009). The peak values occur when Cr = 1.0 ([C.sub.sl]/[C.sub.g] = 1); i.e., when the heat capacity rate of the solid is equal to the heat capacity rate of the moist air.

These results show that for NTU [greater than or equal to] 5.0, the maximum effectivenesses in the run-around system will occur at a heat capacity ratio that depends on the operating conditions. The value of [C.sub.sl]/[C.sub.g] that results in the peak effectiveness is different for different operating conditions because the relative magnitudes of the heat and moisture transfer rates change as operating conditions change. The three operating conditions presented in this research and their corresponding optimal values of [C.sub.sl]/[C.sub.g] are: (i) no moisture transfer in sensible heat exchangers ([C.sub.sl]/[C.sub.g] = 1), (ii) moderate moisture transfer at ARI (2005) winter test conditions ([C.sub.sl]/[C.sub.g] = 2), and (iii) high moisture transfer at ARI summer test conditions ([C.sub.sl]/[C.sub.g] = 3.3). These results show that as the amount of moisture transfer increases, the optimal value of [C.sub.sl]/[C.sub.g] increases. This means that in practical HVAC applications of solid desiccant run-around systems, the value of [C.sub.sl]/[C.sub.g] needs to be modified as outdoor conditions change. Since the flow rate of the ventilation air is nearly constant in most HVAC systems, the flow rate of the solid desiccant will need to be controlled in order to maintain optimal performance of the energy recovery system as the weather changes throughout the year.

Figure 10 shows the air inlet and outlet conditions for the supply air and exhaust air exchangers on a psychrometric chart for ARI summer and winter conditions (ARI 2005) when the run-around system is operating at the optimal [C.sub.sl]/[C.sub.g] value during each operating condition. Figure 10 clearly shows that the outdoor supply air is cooled and dehumidified in the summer and heated and humidified in the winter.

[FIGURE 10 OMITTED]

THE THICKNESS OF COATING

In order to investigate the influence of the desiccant coating thickness on the effectiveness of the run-around system, the outside diameter of the desiccant-coated fiber (D) is held constant to keep the specific surface area of the coated fiber used in the porous solid constant. Meanwhile, the diameter of the fiberglass (d) is allowed to change from 10 [micro]m to approaching D = 30.6 [micro]m, which is the outside diameter of the desiccant coating calculated by the solid volume fraction listed in Table 1. This range of d gives a range of desiccant coating thickness from 10.3 [micro]m to nearly 0 [micro]m, desiccant volume fractions from 0.5% to 0%, and fiber volume fractions from 0.1% to 0.9%.

Figure 11 shows the moisture transfer rate, moisture content in supply side inlet and outlet, and effectivenesses versus fiber diameter with NTU = 10, and the heat capacity ratio Cr = 0.3 ([C.sub.sl]/[C.sub.g] = 3.3) for ARI (2005) summer test conditions.

These simulations show that the moisture transfer rate between air and solid desiccant is almost constant as the fiber diameter increases from 10 [micro]m to about 28 [micro]m (or as the desiccant coating thickness decreases from 10.3 to 1.3 [micro]m). As d increases above about 28 [micro]m, the moisture transfer rate decreases rapidly as d approaches D = 30.6 [micro]m. Figure 11b shows that the difference between the solid moisture content in supply side inlet and outlet increases as d increases (or the thickness of the desiccant coating decreases). This is logical because there is less desiccant to store the moisture as d increases, and therefore the moisture content of the desiccant changes more as it flows through the energy exchanger. Here the increased difference between the moisture content of the desiccant in the inlet and outlet can keep the moisture transfer rate nearly constant as d increases, but when d is larger than about 28 [micro]m, the desiccant is too thin to maintain the constant moisture transfer rate, and the moisture transfer rate decreases to a very small value. Figure 11c shows that the sensible, latent, and total effectivenesses are almost constant from d = 10 [micro]m to about d = 28 [micro]m and decrease rapidly after d = 28 [micro]m. In this case, if the coating thickness of the desiccant is larger than 1 or 2 [micro]m, the run-around system has almost the same performance no matter how thick the desiccant coating is.

Similar results were obtained for the ARI (2005) winter test conditions but are not presented graphically. The only major difference between the summer and winter test conditions is that the critical thickness of the desiccant coating is smaller during winter operating conditions because the moisture transfer rate is smaller due to drier air conditions. For the silica gel particle with a diameter of about 0.5 to 5 [micro]m, if the fiberglass is covered by this desiccant completely, the thickness of coating should be thick enough for the moisture transfer in the run-around system.

SENSITIVITY STUDIES

The purpose of the sensitivity study is to investigate how the effectiveness will change with changes in NTU, air velocity, silica gel fraction, and porous moving balls. These results can demonstrate how the performance of this solid desiccant run-around system will change during practical use.

NTU

It was shown previously that for each specific NTU value, the effectiveness will be close to a maximum when Cr = 0.3 ([C.sub.sl]/[C.sub.g] = 3.3) during ARI (2005) summer conditions and when Cr = 0.5 ([C.sub.sl]/[C.sub.g] = 2) during ARI (2005) winter conditions. Figure 12 shows the peak effectivenesses of the run-around system versus NTU with heat capacity ratio Cr = 0.3 ([C.sub.sl]/[C.sub.g] = 3.3) for the ARI summer test conditions and heat capacity ratio Cr = 0.5 ([C.sub.sl]/[C.sub.g] = 2) for the ARI winter test conditions. This figure shows the three effectiveness values are nearly the same during the ARI summer test conditions but are different during the ARI winter conditions. For all cases, the total effectiveness lies between the sensible and latent effectiveness. Although they are different during the summer and winter ARI operating conditions (for the same NTU), the total effectiveness is almost the same in both the summer and winter conditions when the NTU is the same.

[FIGURE 12 OMITTED]

For a specific NTU, the peak effectiveness values can be found in Figure 12 for summer and winter ARI (2005) test conditions, respectively. In order to achieve a high effectiveness, the NTU should be high. For example, when NTU = 15, the total effectiveness from Figure 12 is about 70% for both summer and winter test conditions. This high value of NTU can be obtained with a large surface area inside the moving solid particle bed. For the 0.3 x 0.3 x 0.3 m (1 x 1 x 1 ft) exchanger used in this paper with a solid (glass fiber + silica gel) volume fraction of 0.6% (Table 1), an NTU of 15 corresponds to a face velocity of about 4 m/s (800 fpm).

Air Velocity and Silica Gel Fraction

Figure 13 shows the effectiveness versus air face velocity and silica gel fraction for ARI (2005) summer conditions and Cr = 0.3 ([C.sub.sl]/[C.sub.g] = 3.3). When the air velocity increases from 0.6 to 2 m/s (120 to 400 fpm), NTU decreases from 35 to 20, approximately. The effectiveness decreases marginally with increasing face velocity for the range investigated.

[FIGURE 13 OMITTED]

For a constant air face velocity of u = 1 m/s (200 fpm), Figure 13b shows that when the silica gel fraction increases from 0.1% to 0.65%, the effectiveness increases with increasing volume fraction of silica gel ([[epsilon].sub.si]). The logic of this is that an increasing [[epsilon].sub.si] increases the surface area for heat and moisture transfer in the porous bed, which increases NTU from around 10 to 35 as [[epsilon].sub.si] increases from 0.1% to 0.65%. This trend in effectiveness change can also be found in Figure 12a when NTU is increased.

Moving Porous Balls

In order to let the porous bed move without mechanical damage to the coating, the fiber and silica gel coating are transported by moving highly porous balls or cages. A schematic of each ball and the run-around system are shown in Figure 14. For this to work in a practical application, the shell or cage of each ball must have a very low flow resistance compared to that of the internal coated fiber material. In addition, the shell or cage must protect the fibers from repeated impact and abrasion during transport between the supply and exhaust exchangers. Although durability of the cage and fibers is an important practical issue, it is not analyzed in this paper. The analysis is limited to the effect that these cages may have on the flow patterns and heat and moisture transfer performance of the run-around system.

[FIGURE 14 OMITTED]

In general, the airflow through porous balls is very complicated, with a flow velocity inside each ball that is not uniform. In the moving porous bed, the differential control volume is [DELTA]x X [DELTA]y, but in the moving porous balls, the differential control volume is a ball with diameter d.

The balls will move steadily through each exchanger along tilted guidance rods. After heat and moisture transfer between the air and solid desiccant inside each ball in the supply side, the balls leave the exchanger and are mechanically conveyed to the exhaust exchanger where they are regenerated. In applications where the supply and exhaust exchangers are close together, the lines in Figure 14 could be tubes slightly bigger than the porous balls. A mechanical arm could periodically push a ball into the tube from the bottom hopper of one exchanger, causing a ball to fall from the other end of the tube and into the top hopper of the other exchanger. In cases where the exchangers are more remotely located, it may be possible to transport the balls using high-speed air, provided that the air is conditioned to the appropriate temperature and humidity. The energy required to transport the balls between the supply and exhaust exchangers will depend on the required capacitance rate and the distance between the exchangers. It is expected that this transportation energy will be a small fraction of the energy transferred by the run-around system; however, it should be considered when analyzing the energy and economic performance of an HVAC system that includes a run-around system.

In the model presented in Part I (Li et al. 2009), it is assumed that all of the air that flows through the energy exchanger exchanges heat and moisture with the porous moving bed; however, when the porous material is contained in a spherical shell or ball, some of the air will bypass the porous material. As the fraction of air that bypasses the ball increases, the total heat and moisture transfer rates (and effectiveness values) will decrease because only the air that passes through the ball will exchange heat and moisture with the desiccant-coated glass fiber. In order to estimate this effect, it is assumed that the fraction of the air flowing through each ball ([f.sub.in, ball]) is constant and that the air passing through each ball and the air bypassing each ball uniformly mix after each ball passes. In addition, it is assumed that the air temperature and vapor density as well as the solid temperature and moisture content inside each ball are uniform because each ball is small compared to the entire exchanger and the balls rotate as they move through the exchanger. This problem is similar, but not identical, to the problem of flow maldistribution in cross-flow air-to-air energy exchangers due to membrane deflections (Larson et al. 2008).

The temperature and density of the air after mixing the air that flows through the ball and the air that bypasses the ball can be calculated from energy and mass balances. Assuming that both airstreams have the same density and specific heat capacity, the mixed-air temperature can be calculated as follows:

[T.sub.g](i,j) = [[[T.sub.g][(i,j).sub.out][Q.sub.out] + [T.sub.g][(i,j).sub.in][Q.sub.in]]/Q] (1)

In Equation 1, the indices (i, j) represent the position of each ball, for example, (1, 1) represents the ball in the first row and the first column, [Q.sub.out] is the airflow rate outside of the ball (or the flow that bypasses the ball), [Q.sub.in] is the airflow rate through the ball, Q is the total airflow rate, [T.sub.g][(i,j).sub.out] is the air temperature outside of the ball, [T.sub.g][(i,j).sub.in] is the average temperature of the air in the ball, and [T.sub.g](i,j) is the air temperature after mixing the airstreams that flow inside and outside of the ball. [T.sub.g][(i,j).sub.in] can be calculated using the same method described in Part I (Li et al. 2009) (i.e., assuming that all the air flowing through the exchanger exchanges heat and moisture with the desiccant-coated fiber or [f.sub.in, ball] = 1). The vapor density of the mixed airstreams can be calculated with

[[rho].sub.v](i,j) = [[[[rho].sub.v][(i,j).sub.out][Q.sub.out] + [[rho].sub.v][(i,j).sub.in][Q.sub.in]]/Q], (2)

where [[rho].sub.v][(i, j).sub.out] is the vapor density of the air that bypasses the ball, [[rho].sub.v][(i, j).sub.in] is the vapor density inside the ball, and [[rho].sub.v](i, j) is the vapor density after mixing the airstreams that flow inside and outside of the ball. Similarly, as with [T.sub.g][(i, j).sub.in], [[rho].sub.v][(i, j).sub.in] can be calculated using the same method described in Part I (Li et al. 2009).

It would be very difficult to correctly estimate the fraction of airflow passing through each ball ([f.sub.in, ball]) and its pressure drop theoretically. In order to investigate how [f.sub.in, ball] influences the effectiveness, Figure 15 shows moving m x n balls for ARI (2005) summer conditions, Cr = 0.3 ([C.sub.sl]/[C.sub.g] = 3.3), and an air face velocity of u = 1 m/s (200 fpm), where m is the number of balls in the airflow direction and n is the number of balls in the direction of the ball movement inside the exchanger. The size of the exchanger changes as m increases. The exchanger is twice as long in the flow direction when m = 60 than when m = 30. It should be noted that the maximum value of [f.sub.in, ball] in Figure 15 is [f.sub.in, ball] = [pi]/4 = 0.785, which is an area-averaged maximum and corresponds to the situation where a uniform velocity approaches the ball and the air that flows through the ball and bypasses the ball is unaffected by the permeability of the porous material within the ball. As the permeability of the porous material within the ball decreases, more air will bypass the ball and [f.sub.in, ball] will decrease.

The overall effectiveness does not change significantly with the increase of [f.sub.in, ball] in the range from 0.4 to 0.785 for every specific m number. After flowing through or around the porous ball, the two parts of air mix together, which can increase the temperature and vapor density difference between the air and solid material in the next ball, which can increase heat and moisture transfer. As a result, [f.sub.in, ball] has a slightly smaller effect for an exchanger that has a longer airflow path (i.e., a larger value of m) than one with a smaller airflow path (i.e., a lower value of m). For [f.sub.in, ball] large, the overall effectiveness is not very sensitive to [f.sub.in, ball]. In future work, [f.sub.in, ball] should be obtained by experimental testing.

For a specific [f.sub.in, ball], the larger the m (or the larger the airflow path in each exchanger), the higher the effectivenesses and the larger the air pressure drop through the moving ball system. In practical applications, an optimized design may be reached by trading off changes in the effectiveness and air pressure drop.

Figure 16 shows the effectivenesses with ball number m x n being 60 x 30, Cr = 0.3 ([C.sub.sl]/[C.sub.g] = 3.3), ARI (2005) summer test conditions and [f.sub.in, ball] = 0.6 for different values of NTU. It should be noted that the NTU values in Figure 16 account for the decreased heat and mass transfer surface areas in each exchanger due to the fact that the desiccant-coated fibers are contained in protective porous balls rather than completely filling each exchanger. The results in Figure 16 are very similar to those in Figure 12a. This shows that NTU is the key parameter governing the effectiveness of the run-around system even for different aspect ratios. It also shows that the performance of a run-around system consisting of moving balls filled with a porous media will be very similar to the performance of an ideal run-around system where the porous bed completely fills each exchanger, provided that the fraction of air bypassing the balls is less than 40%. Therefore, the effectiveness for the moving porous ball system with [f.sub.in, ball] [greater than or equal to] 0.6 can be determined from the figures presented in this paper and generated assuming that the each exchanger is completely filled with porous material. For example, a designer can determine the effectiveness of the moving ball system directly from Figure 12 when the NTU value is known and when less than 40% of the supply and exhaust airflows bypass each ball.

[FIGURE 16 OMITTED]

CONCLUSION

This paper presents the numerical heat and moisture transfer predictions of a single exchanger and a run-around system that employ solid-desiccant moving beds. The temperature and humidity ratio distribution inside a single exchanger can be complex. For example, in a single exchanger, when the air inlet relative humidity is high and the solid desiccant is relatively dry, the air outlet temperature can be higher than that of the air inlet temperature, even though the solid desiccant temperature is lower than the air inlet temperature.

For the same airflow rate in the supply side and exhaust side, the sensible, latent, and total effectivenesses of the run-around system depend on the number of transfer units (NTU), the heat capacity ratio (Cr or [C.sub.sl]/[C.sub.g]), and the operating conditions. For the ARI (2005) summer test conditions, the maximum effectivenesses of the run-around system occur at a heat capacity ratio of approximately 0.3 ([C.sub.sl]/[C.sub.g] [approximately equal to] 3.3). For the ARI (2005) winter test conditions, the maximum effectivenesses of the run-around system occur at Cr [approximately equal to] 0.5 ([C.sub.sl]/[C.sub.g] [approximately equal to] 2). This result differs from that for dry air with only sensible energy changes, where the maximum effectiveness of the run-around system occurs at Cr [approximately equal to] 1 ([C.sub.sl]/[C.sub.g] [approximately equal to] 1).

For the same NTU, Cr, and operating conditions, with constant outside diameter of the silica gel coating, the sensible, latent, and total effectivenesses remain nearly constant and independent of the desiccant thickness until the silica gel coating is thinner than 1 or 2 mm.

The effectiveness for a system of porous moving balls depends on NTU, Cr (or [C.sub.sl]/[C.sub.g]), and operating conditions and can be obtained from moving porous bed effectiveness curves based on NTU, Cr, and operating conditions. The air pressure drop through the porous ball system, the air fraction flowing through each ball, mechanical wear of the balls, and the energy required to transport the balls between remote exchangers need to be investigated in future work.

NOMENCLATURE

C = heat capacity rate, W/K

Cr = heat capacity ratio

D = outside diameter of the desiccant-coated fiber, [mu]m

d = ball diameter, mm; diameter of fiberglass, [mu]m

f = air volume fraction

NTU = number of transfer units

q = airflow volume, [m.sup.3]/s

t = temperature, K

u = velocity, m/s

[X.sub.0] = length of the bed, m

[Y.sub.0] = width of the bed, m

[Z.sub.0] = depth of the bed, m

X* = dimensionless coordinate

Y* = dimensionless coordinate

Greek Symbols

[rho] = density, kg/[m.sup.3]

[[epsilon].sub.g] = volume fraction of gas

[[epsilon].sub.s] = volume fraction of solid; sensible effectiveness

[[epsilon].sub.l] = volume fraction of adsorbed water; latent effectiveness

[[epsilon].sub.t] = total effectiveness

[phi] = relative humidity of the gas at a certain point in the bed

Subscripts

E = exhaust side

f = fiberglass

g = gas including dry air and water vapor

i = ball's position in airflow direction

in = inside flow

j = ball's position in solid flow direction

l = absorbed water

o = overall value for the run-around system

out = outside flow

S = supply side

s = silica gel

sl = mixture of solid and adsorbed water

v = water vapor

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Meng Li, PE

Student Member ASHRAE

Carey J. Simonson, PhD, PE

Member ASHRAE

Robert W. Besant, PE

Fellow ASHRAE

Wei Shang, PhD

Received April 19, 2007; accepted September 15, 2008

Meng Li is a mechanical engineer for Colt Engineering Corp., Edmonton, Canada. Carey J. Simonson is a professor and Robert W. Besant is professor emeritus in the Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada. Wei Shang is a researcher in the Department of Petroleum Engineering, University of Tulsa, Tulsa, OK.
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Author:Li, Meng; Simonson, Carey J.; Besant, Robert W.; Shang, Wei
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Date:May 1, 2009
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