a = d a , O exp -V mem J 3.10xl0-74-l + ^ 28\") 4.17xlO\"8(l + 16k\"A) (2.12) Chen and Peng [63] also used a piecewise correlation: 37 CHAPTER 2 Da = d a , 0 e x P 2^416 2416^ 303 10-10 A_<2 10-10(l + 2Um e m-2)) 2 DI = -40 conditions T W i=T s u r r Td, wi = T s u n Where T s u r r=30 (Case 2) T s u r r=50 (Case 3) T s u r r=70 (Case 4) Streamwise variation in moisture flux As above, with: Qair . DI =1-0 Qair . W l =1-0 Stream wise location ' d , DO 'd.x a This is the maximum dew point allowable to ensure no condensation occurs in the wet side as the temperature drops; limited by humidifier heat loss to the surroundings. b These cases use an oven to impose isothermal conditions. 3.4. Experimental considerations 3.4.1. Measurement technique Figure 3.3 illustrates the dew point measurement technique. In steady state, if the convective velocity of the air/water mixture along the channel is greater than the diffusive velocity of water in air across the channel, then a significant concentration gradient in the y-direction will develop. As a result, the sample probe location on the wall 49 CHAPTER 3 opposite the membrane may measure an artificially low concentration value on the dry side and an artificially high concentration value on the wet side. This effect will become more noticeable further along the channel were concentration gradients grow larger and the mixture is no longer well-mixed. To mitigate this effect, the channel exit stream was partially restricted during measurements to force a larger sample of air/water mixture through the sensing cavity. Sensor reads artificially low on dry side and high on wet side H : C HjO x/L=C (Dry Side Inlet / Wet Side Outlet) x/L=C I x/L=1 C (Wet Side Inlet / Dry Side Outlet) Figure 3.3. The measurement technique showing conceptually the concentration gradients across the channel and their effect on measurement precision 3.4.2. Flow correction As a result of the experimental set up shown in Figure 3.2, one must consider the addition of water when stating the actual wet side flow rate delivered to the membrane humidifier. The amount of added water is quantified, assuming an ideal gas mixture and 100% effective bubbler, via: m H20 Psc\" MW r rH20 m Y V a i r m. (3.1) 50 CHAPTER 3 where P^'20 is the saturation pressure at the bubbler temperature, and P is the total pressure in the bubbler. The mass flow rate of water and air are summed to determine the actual flow composition and rate delivered to the membrane humidifier. For reference, Figure 3.4 has been included to show the appropriate correction factors (either volumetric or gravimetric) to obtain the total flow rate of the mixture. Higher backpressure build up at the saturation bubbler results in less water being evaporated by the flow. Should one not account for these corrections, the maximum error will be found in cases with high dew point and high flow rates (which cause higher back pressures). The sensitivity to dew point is much higher than to bubbler pressure. n — ' — i — i — i — ' — i — • — i — • — i — ' — r ~ 20 30 40 50 60 70 80 Dew Point Setting [ °C] Figure 3.4. Volumetric and mass flow rate correction factors due to addition of water for various bubbler backpressures 3.5. Results and discussion 3.5.1. Heat loss to surroundings The amount of heat lost to the surroundings was quantified by how it affects the temperature profiles in co-flow operation with both inlet streams flowing dry air at the 51 CHAPTER 3 same temperature. Neglecting changes in potential or kinetic energy, the heat loss per unit length for this configuration, q' [W m\"1], was calculated according to the equation: , d(mc T) . dT q = —-— = -mc (3.2) dx dx The derivative of the quadratic fit (R = 1.00) shown in Figure 3.5, the appropriate flow rate, and the specific heat capacity of dry air (cy=1007 J/kg/K) were used to calculate the heat loss rate. If the heat loss to the surroundings is modeled with an overall heat transfer coefficient, the following equation applies [69]: q'=Uw(T-T) H v i u r r ; 1 (3.3) The product of overall heat transfer coefficient, U, and effective perimeter, w, can be extracted from the slope of a linear fit in a plot of q' vs. (Tsurr - T)(Figure 3.6). 0.00 0.25 0.50 0.75 1.00 Dimensionless Location (x/L) Figure 3.5. The temperature profile and the heat loss rate to surroundings with dry air in coflow mode (1.0 S L P M ) 52 CHAPTER 3 10 £ 8 ' C C 13 O 2 — i — • — i — • — i — r — i — • Heat Loss Data Linear Fit Confidence Limits =0.172 X Y =0.149 X Y ^ C ^ X 10 20 30 40 50 60 70 (T \"T) [°C] Figure 3.6. Determination of overall heat transfer coefficient A value of Uw = 0.149 ±0.023 W K~ym'1 at a 95% confidence interval was obtained for this particular experimental setup. The Uw term can be assumed constant for fully developed laminar flows because the Nusselt numbers, thermal conductivity of air, and consequently convective heat transfer coefficients all remain approximately constant. 3.5.2. Effect of unbalanced flow rates on humidification performance Reporting solely the outlet dew point or relative humidity, as done in [19], as the performance variable can be misleading because it is possible and common to find that a lower outlet dew point at a higher flow rate can represent more mass of water transferred than a higher dew point reading at a lower flow rate. Therefore, the average water flux across the membrane and latent effectiveness (LE) performance indicators are also considered in the current section. The water recovery ratio (WRR) is not suitable as an effectiveness measure as LE for this study because the dry side and wet side flow is not always balanced (equal). The theoretical maximum amount of transferable water is limited by what can be carried in the stream with the lowest flow rate. Contours of these three metrics for the ranges of flow studied are shown in Figures 3.7-3.10. 53 CHAPTER 3 Figure 3.7. C A S E 1 (Non-Isothermal) - Measured effect of flow rates on a) Outlet dew point, b) Average water flux, and c) Latent effectiveness Figure 3.8. C A S E 2 (Isothermal, 30C) - Measured effect of flow rates on a) Outlet dew point, b) Average water flux, and c) Latent effectiveness 54 CHAPTER 3 Case 3 - Dl: T=50°C, T = -40°C / Wl: T=50°C, T,=50°C / T =50°C „ d d (UTT Dry Side Air Flow Rate Dry Side Air Flow Rate Dry Side Air Flow Rate Figure 3.9. C A S E 3 (Isothermal, SOC) - Measured effect of flow rates on a) Outlet dew point, b) Average water flux, and c) Latent effectiveness Case 4 - Dl: T=70°C, T = -40°C / Wl: T=70°C, T =70°C / T =70°C ———— d ' d surr Dry Side Air Flow Rate Dry Side Air Flow Rate Dry Side Air Flow Rate Figure 3.10. C A S E 4 (Isothermal, 70 C) - Measured effect of flow rates on a) Outlet dew point, b) Average water flux, and c) Latent effectiveness Two observations can be made with regard to Figures 3.7a, 3.8a, 3.9a, and 3.10a. First, in all cases the outlet dew point increases at lower dry side flow rates. This result might be expected since lower flow rates give both the dry gases a longer residence time in the channel, allowing for more moisture to be evaporated from the membrane surface. Second, the effect of the dry side flow rate on outlet dew point is generally much more pronounced than the wet side flow rate (evidenced by the near-vertical contour lines). 55 CHAPTER 3 This suggests that an abundance of moisture exists at the membrane interface on the dry side and it is only the dry side's time in the channel that limits how much water is evaporated. Translating this to a practical design consideration, a bypass gate or bleed valve that reduces the wet side flow rate through the humidifier will reduce the pressure drop through the wet side with minimal loss in moisture transfer performance. Figures 3.7b, 3.8b, 3.9b, and 3.10b uncover no clear trends from case to case. However, it should be noted that a higher outlet dew point does not necessarily mean that more moisture has been transferred (in many cases the opposite is true). This is an important consideration when comparing performance data because using dew point alone may lead to erroneous interpretations. For example, Park et al [19] concluded that flux across the membrane increases with an increase in flow rates, whereas Ge et al [43], in a similar application, concluded that the outlet dew point decreases with increasing flow rates. The two conclusions appear in conflict, but are solely the result of the metric used to indicate performance. A second observation with respect to these graphs is that there exists an optimal combination of flow rates that yields the highest water flux. However, this optimum varies with operating conditions in an unclear way and in some cases is not reliably discernible with the data presented here (Figure 3.10b). Nonetheless, the importance of such information can be illustrated with an example. If operating at 50°C (Figure 3.9b) with both Qair, rj/and Qair, Wi at 1.0 SLPM, bypassing a portion of the dry side flow to allow only 0.7 SLPM through the dry side of the humidifier would enable more water to be transferred. The two streams could then be remixed with a higher specific humidity than if all of the dry air had been passed through the humidifier. 56 CHAPTER 3 A common characteristic on all of the latent effectiveness graphs is a degree of symmetry about a line of equal flow rates (45°C angle on the graphs). This is a consistent trend with sensible effectiveness is heat exchanger technology [61] and is a result of the minimum flow rate limiting the maximum potential water transfer. The implication is that an unbalanced humidity exchanger is more effective than a balanced heat exchanger. Note, however, that a high effectiveness rating (a relative measure) does not necessarily mean the design will meet its performance specification in absolute terms [kg s\" m\" ]. As the temperature increases from Case 2 to Case 4, the LE values become progressively smaller. At equal flows of 0.7 SLPM, the WRR goes from 0.16 at from 30°C to 0.082 at 70°C. The reason for this is because the higher temperature dew points carry a lot more water into the system, but the humidifier is not well-enough designed to transfer a significant portion of it to the dry side. The estimated accuracy (based on sensor accuracy) and precision (standard deviation between replications) of these results are summarized in Table 3.2. At higher temperatures, even small error in measurement can result in large errors in the calculated values of average water flux and latent effectiveness. 57 CHAPTER 3 Table 3.2. Calculated accuracy and precision estimates for dew point readings in factorial experiments A C C U R A C Y 8 [± ° C ] PRECISION b [± °C] Wet Side Dry Side Flow Rate [SLPM] Dry Side Flow Rate [SLPM] [SLPM] 0.4 0.7 1.0 0.4 0.7 1.0 0.4 1.38 1.66 1.94 0.67 0.79 . 0.29 C a s e l 0.7 1.41 1.65 2.07 0.43 0.46 0.03 1.0 1.47 1.79 2.12 0.01 0.50 0.10 0.4 0.80 1.10 1.20 1.20 1.22 1.67 Case 2 0.7 0.71 0.99 1.18 1.09 1.00 0.84 1.0 0.70 0.91 1.17 0.40 0.57 0.14 0.4 0.90 1.32 1.44 0.35 0.55 1.82 Case 3 0.7 0.86 1.09 1.37. 1.07 1.44 1.18 1.0 0.85 1.00 1.33 0.40 1.01 0.66 0.4 1.22 1.46 1.71 1.50 1.17 0.95 Case 4 0.7 1.10 1.51 1.70 0.38 1.78 0.57 1.0 1.20 1.49 •1.72 0.48 1.47 . 1.01 a Based on manufacturer's published accuracy limits for given conditions. b Based on standard error of three replications. . 3.5.3. Stream wise variation in moisture flux The measured dew point profiles and calculated mass flow of water (via Eqn.(3.1) with P„20 replaced with the water vapour partial pressurePH20) are shown in Figures 3.11 to 3.14. For these figures, the arrows indicate direction of flow and the error bars shown are the manufacturer's stated accuracy limits or the standard deviation of the replications, whichever is higher. a) Measured Dew Point Profile b) Calculated Mass Flow of Water 35-30-25-20-P 1 5 ' 1 5-I OH c -5--10 -15-• Wet Side O Dry Side 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless Location (x/L) 5.0x10'\"-4.5x10\"\"-to 4.0x10'\"-\"o 3.5x10\"°-c c CO 3.0x10 s-sz O 2.5x10'\"-c *D Tmem P 0.622 ° T mem (A.6) ^ mem 0.622 and w„„„ -1 - C + c/, w mem (A.7) 1 - C + Cld)D / Tmem This provides a set of 7 equations, 2 of which are non-linear. A subroutine was written in M A T L A B to solve these equations in order to demonstrate an example. The parameters used and solution variables are listed Table A . 1. Table A . l . Example analysis Parameter Value Variable Solution P hw hD D.. t mem c 101325 Pa 40°C 0.03 0.01 0.005 kgrrf's\"1 0.005 kgm-'s\"1 2.0xl0\" 7 kgm-'s\"1 1.75x10-\" m 2 0.30 CO u CO, u J w mem W mem W mem D mem D mem D mem 3.67x10\"3 kgm-'s\"' 0.0227 kg H 2 0 (kg air)\"1 52.3 % 0.1063 k g H 2 0 (kg mem)\"' 0.0173 kg H 2 0 (kg air)\"' 39.7 % 0.0742 k g H 2 0 (kg mem)\"' a - A n isothermal condition is considered here. Eventually different temperatures could be used for the wet and dry sides. \" 109 APPENDIX A In the model presented in this work, this set of equations should be solved at every station along the channel (in the x-direction). The manner in which this could be incorporated into the e-NTU method has not been determined. The £-NTU would eliminate the need to solve the equations at each station. 110 APPENDIX B B. Derivation of energy equation differential equation Consider the control volume in Figure B.l in the case where only one wall is permeable to water flux: I ' n >B,n|lll|l|l[l1lilH membrane . 1 p i ^ l i l l l i i 1 : 4 in » 4 Mwhf W S E i i ' !::iiW(*