Water Cooling with Air Cooling Tower The most

Water Cooling with Air (Cooling Tower) • The most important operation Liquid (Warm water) Humid air out (Warmed water is cooled by contact with atmosphere air) • The latent heat of water is so large (as compare with sensible heat) L’ 2 TL 2 • Lewis relation applies (Le =1. 0) for the air-water system L’ 2 TL 2 Unknowns TL 1 Gas in: TG 1 , Y’G 1 , H’G 1 Modeling Z Z G’s Tower Knowns TG 1 Cooled water out TL 1 Y’G 1 H’G 1 Gas in (Air)

Water Cooling with Air (Cooling Tower) Humid air Liquid out (Warm water) Energy balance in CV (III): L’CALd. TL=G’s{Csd. TG+[CA(TG-To)-CAL(TLTo)+λo]d. Y’} L’CALd. TL= G’s. Csd. TG+G’sλod. Y’ = G’s(Csd. TG+λod. Y’) H’=Cs(TG-To)+λo. Y’ Cs=CB+CAY’ L’CALd. TL = G’sd. H’ L’ = Constant Tower The sensible heat terms are ignored in comparison with the latent heat d. H’=Csd. TG+λod. Y’ L’CALd. TL ≈ G’sd. H’ L’CAL(TL 2 -TL 1)= G’s(H’ 2 -H’ 1) Cooled water out Operating Line Gas in (Air)

L’CAL(TL 2 -TL 1)= G’s(H’ 2 -H’ 1) (H’i vs Ti) TL 2 Humid air out Liquid (Warm water) 2 Slope=(L’CAL/G’s) max H’ 2 2 1 Slope=(L’CAL/G’s) 1 G’s (min) Cold water out H’ 1 TL 2 Water Liquid Temperature (TL) H’ 2 Tower Enthalpy of air-vapor mixture (H’) Water Cooling with Air (Cooling Tower) Operating Line Equilibrium curve TL 1 H’ 1 Gas in (Air)

Water Cooling with Air (Cooling Tower) Mass transfer: NAMAa. Md. Z= -G’s d. Y’= MAFG[ln(1 -PAi/Pt)/(1 -PAG/Pt)]a. Md. Z = MAk. G(PAi-PAG)a. Md. Z = MBPBmk. Y(Y’i-Y’)a. Md. Z G’sd. Y’ = k. Y(Y’i-Y’)a. Md. Z Energy balance in CV (gas-I): -G’s. Csd. TG= h’Ga. H(TG-Ti)d. Z → G’s. Csd. TG= h. Ga. H(Ti-TG)d. Z Energy balance in CV (Liquid-II): L’CALd. TL= [G’s. CALd. Y’-h. La. Hd. Z](Ti-TL) 0 L’CALd. TL= h. L(TL-Ti)a. Hd. Z If the sensible heat of transfer vapor is ignored: Energy balance in CV (III): L’CALd. TL= G’s. Csd. TG+G’sλod. Y’ ≈ G’sd. H’ L’CALd. TL= h. Ga. H(Ti-TG)d. Z + λo k. Y(Y’i-Y’)a. Md. Z = G’sd. H’

Water Cooling with Air (Cooling Tower) Enthalpy of gas-vapor mixture (H’) Operating Line L’CAL(TL 2 -TL 1)= G’s(H’ 2 -H’ 1) II Liquid d. Z TL Ti H’ 2 TL 1 H’G III TL H’ H’ 1 . Ti I Gas Liquid Temperature (TL) TL 2 TL H’ Ti H’i

Water Cooling with Air (Cooling Tower) L’CALd. TL= h. Ga. H(Ti-TG)d. Z + λo k. Y(Y’i-Y’)a. Md. Z = G’sd. H’ If r = h. Ga. H/(Csk. Ya. M) G’sd. H’ = k. Ya. M[(Csr. Ti + λo. Y’i) – (Csr. TG + λo. Y’)]d. Z Le (Lewis relation) = h. G/Csk. Y a. M ≈ a. H for Air-Water syatem → Le ≈ 1 r = h. Ga. H/(Csk. Ya. M) ≈ 1 H’i H’ G’sd. H’ = k. Ya. M[(Cs. Ti + λo. Y’i) – (Cs. TG + λo. Y’)]d. Z G’sd. H’ = k. Ya(H’i – H’)d. Z

Water Cooling with Air (Cooling Tower) G’sd. H’ = k. Ya(H’i – H’)d. Z Energy balance in CV (Liquid-III): L’CALd. TL= G’sd. H’ = k. Ya(H’i – H’)d. Z = h. La(TL-Ti)d. Z TL H’ Ti H’i Slope = -(h. La/k. Ya) Enthalpy of gas-vapor mixture (H’) Energy balance in CV (Liquid-II): L’CALd. TL= h. L(TL-Ti)a. Hd. Z Ti H’i TL H’ Liquid Temperature (TL)

Water Cooling with Air (Cooling Tower) G’sd. H’ = k. Ya(H’i – H’)d. Z = h. La(TL-Ti)d. Z Integration Ht. G Nt. G = Z t. G = transfer in gas phase

• Average driving force Enthalpy of gas-vapor mixture (H’) Water Cooling with Air (Cooling Tower) • Numerical solutions Ti H’i TL H’ Liquid Temperature (TL) Ht. G Nt. G = Z

Enthalpy of gas-vapor mixture (H’) Water Cooling with Air (Cooling Tower) t. OG = transfer overall in gas phase H’* Ti H’i TL H’ Liquid Temperature (TL) ↑ ↑ Ht. OG Nt. OG = Z

Water Cooling Tower Important thing in cooling tower modeling: Liquid (Water) Air out Tower Wet-Bulb Temperature Approach 2. 5 -5 o. C Water out TL 1 TW 1 Gas in (Air)

Water Cooling Tower • Evaporation Losses (E) • Windage Losses (W) Warm Water Blowdown (xo) (0. 1 -0. 3% of L) • Make Up (M) • Blowdown (B) Mass balance: M=E+W+B xi. M=xo(W+B) Air out Evaporation Losses Plant (Q) Windage Losses Make up (xi) Cold Water Gas in (Air)

The sensible heat terms are ignored in comparison with the latent heat For 1 kg liquid water (2. 205 lbm) Heat from 32 o. F to 212 o. F Sensible Heat : q. S=m. Cp(T 2 -T 1) Cp for liquid water=4. 2 J/g. K=1 Btu/lbm. R q. S=2. 205*1*(212 -32)=396. 9 Btu Latent Heat (T=32 o. F)=q. L=mλ=mhfg q. L=2. 205*1075. 8=2372. 1 Btu