Gs-Vpor Mixtures Air is mixture of nitrogen nd oxygen nd rgon plus trces of some other gses. When wtervpor is not included, we refer to it s dry ir. If wter-vpor is included, we must properly ccount for it. Usully, we will consider ir nd wter-vpor (even if wter-vpor is t the sturtion stte) s idel gses. The error using this ssumption will be round 0.2%. Therefore, from Dlton s lw: The totl pressure is the sum of the prtil pressure P of the dry ir nd the prtil pressure P v of wter-vpor (clled vpor pressure): P= P + P v Since we ssume the wter-vpor s n idel gs, its enthlpy is only dependent on the temperture. Therefore, we will consider the enthlpy of wter-vpor s the enthlpy of sturted wter-vpor t the sme temperture. h ( ) ( ) v T = hg T This pproch is cceptble for situtions in which the pressure is reltively low (ner tmospheric pressure) nd the temperture is below bout 60 C. 13.1. Some definitions: 13.1.1. Reltive humidity It is the rtio of the mss of wter-vpor m v to the mximum mount of wter-vpor m g the ir cn hold t the sme temperture. m φ = m v g Gs-Vpor Mixtures nd Air Conditioning 59
using idel gs lw: PV / R T P PV / RT P v v v φ = = with φ between 0 nd 1. g v g 13.1.2. The humidity rtio ω (specific humidity): It is the rtio of the mss of wter-vpor to the mss of dry ir: mv ω = m using idel gs lw: PV v / RvT Pv / Rv ω = = PV / RT P / R but: R v =0.4615 kj/kmol K R =0.287 kj/kmol K Pv Pv Therefore: ω = 0.622 = 0.622 P P Pv And using the reltive humidity: φpg ω = 0.622 P Exmple AIR 25 C, 1 tm m =1 kg m v =0.01 kg m v, mx =0.02 kg Specific humidity: ω=0.01 kg H 2 O/kg dry ir Reltive humidity: 50%. 13.1.3. Dry bulb temperture: It is the temperture of the ir s mesured by conventionl thermometer. 13.1.4. Dew-point temperture (T dp ): It is the temperture t which condenstion begins if ir is cooled t constnt pressure. Figure.13.1. Dew-point temperture. Gs-Vpor Mixtures nd Air Conditioning 60
Exmple The ir t 25 C nd 100 kp in XXX m 3 room hs reltive humidity of 60%. Clculte: c- The humidity rtio. d- The dew point. e- The mss of wter-vpor in the ir. 13.1.5. Adibtic sturtion nd wet-bulb temperture It is quit difficult to ccurtely determine directly the reltive humidity nd the humidity rtio. However, two indirect methods exists: - Adibtic sturtion process. - Wet bulb temperture. 13.1.5.. Adibtic sturtion process This method uses reltively long insulted chnnel. Air with unknown reltive humidity (ω 1 ) enters, moisture is dded to the ir by the pool of wter, nd sturted ir exits. This process involves no het trnsfer becuse the chnnel is insulted. Figure.13.2. Adibtic sturtor. An energy blnce on this control volume, neglecting kinetic nd potentil energy chnges, with Q=W=0, gives: m& h + m& h + m& h = m& h + m& h but v1 v1 1 1 f f 2 2 2 v2 v2 m& = m& = m& 1 2 m& + m = m& v1 using ω: f v2 m& ω + m& = m& ω 1 f 2 Gs-Vpor Mixtures nd Air Conditioning 61
substituting with, h v h g m& ω h + mh & + ( ω ω ) mh & = mh & + ω mh & 1 g1 1 2 1 f 2 2 2 g2 but t stte 2, φ 2 =100%. Pg 2 So: ω 2 = 0.622 P P And, g 2 ( ) ω h + C T T ω1 = h h 2 fg 2 p 2 1 g1 f 2 To know ω 2, we hve to mesure T 1 nd T 2 nd the totl pressure P. The problem with dibtic sturtion process is tht it requires long chnnel to chieve sturtion conditions t the exit. Note: usully the mount of dry ir in the ir-wter-vpor mixture remins constnt, but the mount of wter-vpor chnges. Therefore, the enthlpy of tmospheric ir is expressed per unit mss of dry ir insted of per unit of ir-wter-ir mixture. 13.1.5.b. Wet bulb temperture A much simpler pproch is to wrp the bulb of thermometer with cotton wick sturted with wter. Then, we cn blow ir over the wick or swing the thermometer through the ir until the temperture reches stedy stte: this is the wet-bulb temperture. The dibtic sturtion temperture is essentilly the sme s the wet-bulb temperture if the pressure is pproximtely tmospheric. Figure.13.3. dry-bulb nd wet bulb tempertures. Exmple The dry nd the wet-bulb tempertures of tmospheric ir t 1 tm (101.325 kp) pressure, mesured using n dibtic sturtion process re 15 C 25 C respectively. Determine: - The specific humidity. b- The reltive humidity. Gs-Vpor Mixtures nd Air Conditioning 62
13.2. Aditionl informtion: # Actul method to dermine the reltive humidity nd the humidity rtio: Actully new devices bsed on the cpcitnce chnge of thin polymer film re used to detemine ω nd φ. # Did you know tht hir length increses with humidity? The rnge between dry nd sturted ir cn ccount for difference in hir length of bout three per cent. In moist ir, people with nturlly curly hir experience the frizzies s their hir increses in length. Under the sme conditions, people with long, stright hir find it going limp. Hir is such relible indictor of good or bd wether, in fct, tht it is the primry element of the hir hygrometer, n instrument tht ws used for yers to mesure humidity. Invented in 1783, it ws used until more sophisticted technology ws developed in the 1960s. For its time, it ws very ccurte humidity-mesuring device, lthough not in widespred meteorologicl use tody. # Humidex fctor: "The humidex is Cndin innovtion, first used in 1965. It ws devised by Cndin meteorologists to describe how hot, humid wether feels to the verge person." The humidex is bsed on the observtion tht intense het ccompnied by high vpour content, bring bout physicl mlise. In extreme cses, when the combined effects of the temperture nd moisture pproch the norml temperture of the body (37 C), this mlise becomes dngerous for the humn body. H = T + (5 / 9)(P v - 10) H is humidex index, T is temperture in C, P v is the wter vpor pressure in millibr (mbr)} Gs-Vpor Mixtures nd Air Conditioning 63
Rnge of humidex Degree of comfort Less thn 29 No discomfort 30 to 39 Some discomfort 40 to 45 Gret discomfort; void exertion Above 45 Dngerous Above 54 Het stroke imminent # Wind chill index: "The originl wind chill formul ws derived from experiments conducted in 1939 by Antrctic explorers, Pul Siple nd Chrles Pssel. These hrdy scientists mesured how long it took for wter to freeze in smll plstic cylinder when it ws plced outside in the wind. Over the yers, the formul ws modified somewht, but remined bsed on the Antrctic experiments." This formul ws obsolete nd in certin circumstnces creted confusion. Rther thn be bsed on wter cylinder, "the new index is bsed on model of how fst humn fce loses het. We chose the fce becuse it is the prt of the body most often exposed to severe winter wether, ssuming the rest of the body is clothed ppropritely for the wether". The wind chill formul is: R = 13.12 + 0.6215 T 11.37 (V 0,16 ) + 0.3965 T (V 0,16 ) where { R is the wind chill index; T is the ir temperture in degrees Celsius ( C); V is the wind speed t 10 metres (stndrd nemometer height), in kilometres per hour (km/h) } 13.3. The psychrometric chrt nd ir-conditioning processes 13.3.1. The psychrometric chrt All the equtions introduced in the upper section re very useful when working t pressures higher thn the tmospheric pressure. For stndrd tmospheric pressure, the most convenint wy to determine the vrious properties ssocited with wter-vpor mixture is to use psychrometric chrt (Fig.13.4). Figure.13.4. Psychrometric chrt (principle). Gs-Vpor Mixtures nd Air Conditioning 60
Exmple Find the dew-point temperture, the wet bulb temperture the enthlpy nd the humidity rtio for the following conditions: - dry bulb temperture (T=30 ) nd reltive humidity of 80%. b- dry bulb temperture (T=35 ) nd reltive humidity of 40%. 13.3.2. Air conditioning processes: Generlly, people feel most comfortble when the ir is the comfort zone : the temperture is between 22 C nd 27 C nd the reltive humidity is between 40% nd 60% (Fig.13.5) (nd usully wind speed 15 m/min). The re enclosed by the hevy dotted lines represents the comfort zone. There re severl situtions in which ir must be conditioned to put it the comfort zone: Problem Solution Representtion The ir is too cold or too hot Het is simply dded or A-C nd B-C extrcted The ir is too cold nd the The ir cn first be heted, nd D-E-C humidity is too low then moisture dded The temperture is cceptble The ir is first cooled, nd then F-G; G-H nd H-I but the humidity is too high moisture is removed. Finlly, the ir is reheted The ir is too hot nd the Moisture is dded J-K humidity is low An irstrem from the outside is mixed with n irstrem form the inside to provide nturl cooling or fresh ir I (inside ir) + L (outside ir) = M (mixed ir) Figure.13.5. The conditioning of ir. Gs-Vpor Mixtures nd Air Conditioning 61
13.3.2.1. Air-conditioning processes nlysis Most ir-conditioning processes cn be modeled s stedy-flow processes. Mss blnce for dry ir: Mss blnce for wter: m = inlet m outlet m v inlet mv = outlet Neglecting ΔE K nd ΔE P, the first lw cn be written s: in + W& in + m& h = inlet Q & m& h + Q& + W& outlet out out 13.3.2.2. Simple heting nd cooling (ω=c t ) Figure.13.6. Simple heting. Note: the reltive humidity of ir decreses during heting process (φ 2 <φ 1 ) even if the humidity rtio ω remins constnt. This is becuse the reltive humidity is the rtio of moisture content to the moisture cpcity of ir t the sme temperture, nd the moisture cpcity increses with temperture. First lw (neglecting ΔE K nd ΔE P nd usully the work of the fn is lso neglected) cn be written under the simple form: ( ) Q& = m& h 2 h 1 13.3.2.3. Heting with humidifiction: To overcome the problem of decresing φ with simple heting, ir is pssed first through heting section nd then through humidifying section Figure.13.7. Heting nd humidifiction. If stem is used T 3 > T 2 If liquid is used T 3 < T 2 Gs-Vpor Mixtures nd Air Conditioning 62
13.3.2.4. Cooling with dehumidifiction Note tht if the T then φ 13.3.2.5. Evportive cooling Figure.13.8. Cooling nd humidifiction. Dry ir enters the evportive cooler where it is spryed with liquid wter. Prt of the wter evportes during this process by bsorbing het from the strem. As result the temperture decreses nd humidity increses. Figure.13.9. Evportive cooling. Gs-Vpor Mixtures nd Air Conditioning 63
This process is t constnt enthlpy nd constnt wet bulb temperture (constnt enthlpy nd constnt wet bulb temperture lines on the psychrometric chrt re lmost the sme). 13.3.2.6. Adibtic mixing of irstrems In lrge buildings (hospitls, process plnts, ), two strems re usully mixed (mixture of conditioned ir nd new fresh ir). The het trnsfer with the externl medium is smll nd thus the mixing process cn be ssumed s dibtic. Mss blnce for dry ir: m &, 1 + m&,2 = m&, 3 Mss blnce for wter: ω 1m &,1 + ω2m&,2 = ω3m&, 3 Neglecting ΔE K nd ΔE P, the first lw cn be written s: m& & = &, 1h1 + m,2h2 m,3h3 Eliminting m&, gives:,3 m& m&,1,2 ω2 ω3 = ω ω 3 1 = h h 2 3 h 3 h 1 Figure.13.10. dibtic mixing. Therefore, when two irstrems t two different sttes (stte 1 nd 2) re mixed dibticlly, the stte of the mixture (stte 3) will lie on the stright line connecting sttes 1 nd 2 on the psychrometric chrt, nd the rtio of the distnces 2-3 nd 3-1 is equl to the rtio of mss flow rtes t 1 nd 2. Note: if 1 nd 2 re close to the sturtion line, point 3 my lie to the left of this line. As consequence, some wter will inevitbly condense during the mixing process. Exmple Outside cool ir t 15 C nd 40% reltive humidity (irstrem 1) is mixed with inside ir tken ner the ceiling t 32 C nd 70% reltive humidity (irstrem 2). Determine the reltive humidity nd temperture of the resultnt irstrem 3 if the outside flow rte is 40 m 3 /min nd the inside flow rte is 20 m 3 /min. 13.3.2.7. Wet cooling towers In power plnts or refrigertion plnts, the wsted het is usully rejected to the se, lke or river. However, when the wter supply is limited, this het must be rejected to the tmosphere. This is performed using wet cooling tower. Gs-Vpor Mixtures nd Air Conditioning 64
Air is drwn into the tower from the bottom nd leves through the top. Wrm wter from the condenser is pumped to the top of the tower nd is spryed into the irstrem. The purpose of sprying is to expose lrge surfce of wter to ir. As the wter droplets fll under the influence of grvity, smll frction of wter (usully few percent) evportes nd cools the remining wter. The temperture nd the moisture content of the ir increse during this process. The cooled wter is collected t the bottom of the tower nd is pumped bck to the condenser to pick up dditionl wste het (ref. Cengel). Figure.13.10. Wet cooling towers. (left) An induced-drft couterflow cooling tower. (right) A nturl-drft cooling tower. 13.3.3. Additionl informtion The humn body opertes like het engine, the energy input is food (mny thnks to McDO ) nd some wsted energy is ejected to the environment. The rte of het genertion for mn depends on the level of ctivity: Sleeping Resting of doing office work Bowling Hevy physicl effort 87 W 115 W 230 W 440 W For womn, the rte of genertion is less by bout 15% (due to smller body size re). Procedure For Clculting The Properties Of Moist Air 1. Determine wht properties you need to clculte. This depends on the problem. Don't forget tht the Principles of thermodynmics nd the Process descriptions re independent of the method for clculting the Properties. 2. From the Process description, determine the pressure P of the moist ir. This is the pressure tht would be mesured by pressure gge. 3. From the Process description, determine the temperture T of the moist ir. This is the temperture tht would be mesured by n ordinry thermometer or thermocouple. If the temperture is not known, you must solve the problem by tril nd error, so guess vlue. 4. Look up the vlue of the wter vpor prtil pressure t sturtion, P g, using the Sturted Stem Temperture Tble for Wter. 5. If the reltive humidity, phi, is known from the Process description, write it down nd go on to clculting the ctul prtil pressure of the wter vpor in the moist ir, P v, from the eqution Gs-Vpor Mixtures nd Air Conditioning 65
φ = P v / P g Then clculte the humidity rtio, omeg, from the eqution ω = 0.622*P v / (P - P v ) 6. Once omeg is known, you cn clculte the moist ir properties from the equtions given bove. 7. If the reltive humidity (phi) is not known, but the humidity rtio (omeg) is known nd you wnt to know the reltive humidity, you cn clculte P v from P v = ω*p / (ω + 0.622) And then get phi from its definition, φ = P v / P g 8. If neither ω nor φ is known, but the wet bulb temperture T wb is known, then T wb cn be used, long with T db (the dry bulb temperture, where T db = T), to find omeg from the eqution given bove, ω = (c p *(T wb - T db ) + ω g *h fg ) / (h v (T db ) - h f ) Where omeg g is the humidity rtio t sturtion t the wet bulb temperture, T wb, omeg g = 0.622*P g / (P - P g ) Note tht P g, h f, nd h fg re found from the Sturted Stem Temperture Tble t the wet bulb temperture (T wb ). 9. The reltions between ω, φ, T db, T wb, re shown grphiclly on the Psychrometric chrt. The enthlpy nd volume (per unit mss of dry ir) cn lso be found, lthough not very ccurtely, from the chrt, but the entropy is not shown t ll. Gs-Vpor Mixtures nd Air Conditioning 66