Document R2XgxXpBzdp6Dvz5Dkn1rVnbE

84 CHAPTER 5 the latent heat h/,, after making the two preceding assumptions is not warranted. - (4) Energy Balance <7adh , Gveudti (39) A minus agnjrefera to parallel flow of air and water and a plus sign to couoter&owi Actually, the water flow rate changes between inlet and outlet due to the ">** transfer. For exact energy balance the term (ctit^GL) "bonlH be added to the right side ofEquation 39. The percentage change in Gj. Is quite small in all normal ap plications *f nning equipment and,' therefore, may Se (5) Beat Transfer to-the Water G&czdtt " fcrOff(tr. -- (40) Equations 36,to 40 are thebasic relations necessary to the solution of simultaneous heat and mass transfer processes in direct contact air-oonditioning equipment. To facilitate the use of these relations in equipment design or performance, three other equations may be extracted from the above set. Combination of Equations 38, 39, and 40 gives *' 1 h'-h<i-":;'' htAa '' ' ' hi, `i.. to -- U Kdomi Kd Equation 41 relates the enthalpy potential for the total heat transfer through the gas film to the temperature po tential for thi same transfer through the liquid film. As would be expected from physical'reasoning, this ratio is pro portional to the ratio of gas,film resistance, (l/Kp) to toe liquid film resistance (1//l)- Combination of Equations 37, 38, and the Lewis relation (Equation 32) gives ` dh ' h - hi : dU -U (42) ,, Similarly,combination of Equations 36, 37, and theLewis relationj gives dW W -Wt dtT " U - U (43) ` .Equation 43 indicates thatat any, cross section in the spray chamber, the. instantaneous slope of the air path, dW/dt*, on.a. psychrometrie chart is determined by. a straight. line connecting the air state with the interface saturation state at that cross-section. Thus in Fig. 12, state 1, represents the state of the air'entering the parallel-flow air watoer chamber 1965 Guide And Data Book Fig. 13.'... Graphical Solution'for the Air-State Path 1 in a Parallel-Row Air Washer illustrated in Fig. 11. The washer is operating as a heating and'humidifying apparatus so that the interface'saturation state of the water at air inlet is the state designated 1. The initial- slope of-the'air path is, ;tben, along'a line directed from state 1 to state 1,-. As the air is heated, toe water cools and the interface temperature drops. Corresponding air states and interface saturation states are indicated by the letters a, b, c, d in-jig. 12. Note that in each instance the air path is'directed toward the associated interface state. The 'inter face states are found from Equations 39 and '41'. Equation 39 describes how the air enthalpy .changes with water tem perature; and Equation 41, how . the interface saturation state changes to'accommodate'this*chahge'in air and water conditions. The solution for the interface state on the normal psychrometrie chart of Fig. 12 must be either-by trial-and error from Equations 39 and 41 or by a rather complex graphs cal procedure.11 A-much simpler method of solution results by using-the-method1 of Merkel1* with improvements by Mickley.u This 'method utilizes a psychrometrie chart-with enthalpy;and temperature as the coordinates:- It is best illus- trated by example. - . ' Example 8. A parallel'flow air washer is to be designed using s spray chamber like that illustrated in Fig. 11. The deeign-cohditoons are as follows: - Water temperature at inlet, tu = 95 F- - . Water temperature at outlet,'toi-= 75 F Air temperature at inlet, to = 65 F .- Air wet-bulb at inlet, to' -- 45 F ; Air mass flow rate per unit area, O. = 1200 lb per (hr) (sq ft) -- Spray ratio, 0.70 Mass Transfer 85 of- the air leaving the chamber is reached.. In this example six steps are used in the. graphical construction with'the following results: State to b U h. '1 95.0 17.65 84.5 49.00 65.0 'a 91.0 20.45 82.3 46.25 66.8 b 87.0 23.25 80.1 43.80 68.5 83.0 26.05 77.8 41.50 70.0 d 79.0 28.85 75.6 39.10 71.4 2 75.0 31.65 73.2 37.00 72.4 Air transfer coefficient per cubic foot of chamber volume, Kas = 72 Btu per (hr) (F deg) (cu ft) ' liauid - hfi*t transfer coefficient per cubic foot of chamber' volume, kioa =* 900 Btu per (hr) (F deg) (cu ft) Air volume flow rate, Q - 6500 cfm Solution: The air miua flow rate ta. = (6500/13.25) ='490 ib/min, and the required spray chamber cross-sectional area is, then Aa - w./G. - 490 (60)/1200 = 24.5 sq ft. The mass transfer coefficient is given by toe Lewis relation as Knojr - (Mrl/to - 72/0.24 - 300 lb per (hr)(cu ft) .. Fig. 13 shows the enthalpy-temperature psychrometrie chart with the graphical solution tor the interface states and the airpath through the washer spray chamber. The solution proceeds as follows: 1. Enter bottom of chart with to' of 45 F, follow up to satura tion curve to establish air enthalpy hi of 17.65 Btu/Ib. Extend this enthalpy line to'intersect initial air temperature to of_65'F (state 1 of air), and initial water temperature tu of 95 F at point,, A. (Note carefully hero that wc utilise the temperature scale both for air and water temperatures.) 2. Through point A construct the energy balance line AB with a slope of (dh/dlL) - - Gl/G. " - 0.7 Point B is determined by intersection with the leaving water temperature tu = 75 F. The negative slope here is a consequence of the parallel Sow, which results in the air-water mixture ap-' reaching, but not reaching, the common saturation state t..(Tne line AB has no physical significance as far as representing any air state on tiie psychrometrie chart. It is merely uyd as a construc tion line in the graphical solution.) - > > ; 3. Through point A construct the'fie-Jtne AU having aslope of h -- h, ht/iB `900 \ to -- ti Room 300 . .'?*? intersection of this line with the saturation curve gives the'4tial interface state 1,- at the chamber inlet. (Note carefully "*re how the energy balance line and tie-line, representing Equa- tooos 39 and 41, are combined to give a simple graphical solution' on the A -- t chart for the interface state.) 4. The initial slope of the air path may now be constructed, ae- W"hig to Equation 42, by drawing line la toward the initial Ptoface state 1<. (The length of theune la will depend upon the uegree of accuracy required in the solution and the rate at which the slope of the air path is changing.) <k5* ^0D8^uc^ the horizontal line a-M locating the point M on the energy-balance line. Draw a new tie-line (slope of -- 3 as w r "m ^ to a,- locating interface state <n. Continue the air JSTM a to b by directing it toward toe new interface state e*. in.ote that the change in slope of the air path from la to ab is quite small, justifying the path incremental lengths used.) 6. Continue in the manner of step 5 until point 2, to** state `The final state of the air leaving the washer is to * 72.4 F and hj -- 31.65 Btu per lb (wet-bulb temperature to' = 67.0 F). 7. The final step is to calculate the required length of the spray chamber. From Equation 38b G. r1 dh Kpatt J i (hi -- h) . The integral is evaluated graphically by plotting l/(h< -- h) ra b as shown in Fig. 14. Any satisfactory graphical method may be used to evaluate the'area under the curve. Using Simpson's rule with four equal increments of Ah equal to 3.5 gives: -J*N-= ^ ^ -(Ah/3)(yi + 4yi + 2yt + 4y, + y*) N - (3.5/3){(l X 0.0319) + (4 X 0.0400) + (2 X 0.0553) . + (4 X 0.0865) + (1-X 0.1870)] - 0.975 ' '* The design length is, therefore, l = (1200/300)(0.975) = 3.9 ft. Tbe method illustrated by Example 8 may be also used to predict the performance of existing direct-contact equipment. Furthermore, the method can serve the very-important func-, tion of determining the transfer coefficients when perform ance data from test runs are available: That is, knowing the water'and air temperatures entering and leaving the'chamber and the spray ratio, it is possible by a trial and error procedure - to'determine'the proper slope of the tie-line necessary to' achieve the measured final air state/ The tie-line slope gives' the ratio hiAB/KoaM- Furthermore, Kpau is determined from' toe integral! relationship in Example 8 from the known chamber length'!. . Rg. 15.... Graphical Solution for the Air-State Path in a Direct-Expansion Coil Dehumidifier