Moisture transfer Csaba Szikra senior research fellow TUB Faculty of Architecture Department of Building Energetics and Services

Transcription

1 Moisture transfer Csaba Szikra senior research fellow TUB Faculty of Architecture Deartent of Buildin Eneretics and Services 2014

2 Psychroetry Moist air Psychroetry involves the study of the roerties of oist atosheric air, the basic ediu in buildin hysics and air-handlin ractise a binary ixture of dry air and low ressure water vaour. Atosheric air is a ixture of dry air and any aount of water vaor. Coosition of dry air are Nitroen, Oxyen, Aron, Carbon dioxide and others. The aount of water vaor in oist air is variable, ranin fro nearly zero to axiu 30 water vaor er k dry air deendin on teerature and ressure at saturation. Moist air is treated as a ixture of indeendent erfect ases, each obeyin the erfect as equation of state.

3 Psychroetry Dalton s Law The air in the atoshere and within buildins ay be considered as a two-coonent as ixture of dry air and water vaour. Take the box heretically divided by a artition. One art contains air as olecules, the other art oisture ones. The ressure on the box wall is roortional to the nuber of olecules. Let us reove the heretic artition. Now, both ases strive to coletely fill the whole box caacity, as if the other as were non existent. The box wall is acted uon by ressure fro both ases: the ressures of the oisture and air ases a and are roortional to the nuber of oisture and air olecules, resectively. Dalton's law (also called Dalton's law of artial ressures) states that the total ressure exerted by a aseous ixture is equal to the su of the artial ressures of each individual coonent in a as ixture. This eirical law was observed by John Dalton in 1801 and is related to the ideal as laws. In buildin enineerin only an atosheric air considered as as ixture of dry air and oisture, thus: 0 a 0 is an overall ixture ressure of dry air and oisture P a are the ressure of the coonents or artial ressure of the coonents

4 Psychroetry Moisture content () a Moist air is a two-coonent ixture of dry air and water vaour. Moisture content of a oist air is defined as the ratio of the ass of water vaour to the ass of dry air. Moisture content is exressed as the nuber of kiloras of water vaour er kilora of a dry air (/k, k/k). The aount of water vaour varies fro zero (dry air) to a axiu that deends on teerature and ressure. a R R a a Substitutin ideal as equation to the definition of oisture content, exressin a by 0 - and substitutin secific as constant of air and oisture, oisture content can be exressed by artial ressure of the oist.

5 Psychroetry Saturation vaour ressure ( s ) s P s [P a] Saturation Pressure t t[ C ] The axiu vaour ressure which can exists in any iven teerature is the saturation vaour ressure. Under this condition the water vaour in the ixture can coexist in neutral equilibriu with surface of water at the sae teerature and the oist air said to be saturated with vaour. Saturation vaour ressure is a function only of teerature and is indeendent of the dry air which siultaneously occuies the sae sace. The value of saturation ressure is iven in s -t diara or stea tables. in s -t diara is often used for describin oisture behaviour of coosite buildin aterials. Saturation ressure can exressed (based on the reviously develoed equation) by oisture content: s

6 Psychroetry Relative huidity S aturation P ressure P s [P a] s t[ C ] Relative huidity is defined as the ratio of the artial ressure of water vaor in a aseous ixture of air and water vaor to the saturated vaor ressure of water at a sae teerature. That is, a ratio of how uch enery has been used to free water fro liquid to vaor for to how uch enery is left. Relative huidity is exressed as a ercentae and is calculated in the followin anner: RH s ( t) ( t)

7 Psychroetrics dew oint S aturation P ressure P [P a] s t[ C ] The dew oint is the teerature to which a iven arcel of huid air ust be cooled, at constant baroetric ressure, for water vaor to condense into liquid water. The condensed water is called dew when it fors on a solid surface. The dew oint is a saturation teerature. The dew oint is associated with relative huidity. A hih relative huidity indicates that the dew oint is closer to the current air teerature. Relative huidity of 100% indicates the dew oint is equal to the current teerature and the air is axially saturated with water. When the dew oint reains constant and teerature increases, relative huidity will decrease.

8 Psychroetrics dry and wet bulb teeratures The dry-bulb teerature is the teerature of air easured by a theroeter freely exosed to the air but shielded fro radiation and oisture. In construction, it is an iortant consideration when desinin a buildin for a certain cliate. It one of "the ost iortant cliate variables for huan cofort and buildin enery efficiency". Assann s sychroeter Wet-bulb teerature the teerature read fro wet bulb theroeter; Wet-bulb teerature is easured usin a theroeter that has its bulb wraed in cloth called a sock that is ket wet with water via wickin action. Such an instruent is called, a wet-bulb theroeter. At relative huidities below 100%, water evaorates fro the bulb which cools the bulb below abient teerature. To deterine relative huidity, abient teerature is easured usin an ordinary theroeter, better known in this context as a dry-bulb theroeter. At any iven abient teerature, less relative huidity results in a reater difference between the dry-bulb and wet-bulb teeratures; the wet bulb is colder. The recise relative huidity is deterined by findin one's wet-bulb and dry-bulb teeratures on a sychroetric chart

9 Psychroetrics Secific Enthaly (h) heat content er unit ass, is the su of the internal (heat) enery of the oist air in question, includin the heat of the air and water vaor within h c t ( c t r0) 1 a c a Secific heat of dry air at constant ressure [kj/kk] = 1 c Secific heat of overheated stea at constant ressure [kj/kk] = 1.86 r 0 secific enthaly of water[kj/k] = 2500

10 V in in in ax Moisture balance of an internal environent ( / h) w ( / h) ( / h) V in w in out w out out in in out out V w V out out ρ (k/ 3 ) Density of the air = 1,2 in (/k) vaour quantity er unit volue of the enterin air out (/k) vaour quantity er unit volue of the leavin air w (/h) oisture arisin fro internal source V( 3 /h) Volue flow rate of echanical or natural ventilation Moisture develoent is the consequence of the resence and activity of occuants. Obviously excessive oisture develoent increases the risk of daae to be iarted to dwellers and oerators of the buildin, but of course, oisture develoent cannot be reduced below a threshold without detrient to the buildin's roer use. Main oisture sources: Occuancy 40/h,ers Dryin, lants, cleanin, washin, showerin 25l/ers/week in / h w / h out / h Most of the oisture arisin in the roo leaves with the ventilation air. There is also vaour diffusion across walls and floors, however, for oisture balance in a roo, the quantity of oisture leavin by diffusion is neliible. Note, that saturation liit deends on teerature, so at a low teerature a rather low (absolute) huidity causes a hih relative huidity, while at a hih teerature, for a coaratively low relative huidity there is a hih absolute huidity.

11 Vaour transfer Mechanis of vaour trasfer Let us take a box divided by a artition. Let its resective divisions contain different as ixtures of air as and oisture olecules. The overall ressures on the artition are equal, but on one side, artial ressure of the air as, on the other side, that of the oisture as is the hiher. If the artition is not coletely tiht but as olecules can ass throuh, then the difference between artial ressures of the air as as akes air as as to flow to the oosite division, and so does oisture as, in site of the overall ressures of the ixtures bein equal. This is the backround (the drivin echanis) of the vaour diffusion throuh buildin eleents.

12 Saturation Pressure Vaour trasfer Scoe of calculation P s [P a] Due to the different indoor and outdoor air conditions, enerally there is a difference between the artial water vaour ressures in indoor and outdoor air. This ressure difference is the drivin echanis of vaour flow (usually called diffusion) throuh ereable buildin eleents. Note that only the artial water vaour difference is soken about. The baroetric ressure of the indoor and outdoor oist air are the sae. Certainly, at equal baroetric ressures, if the vaour ressure is hiher inside, the artial ressure of the dry air is hiher outside and in the oosite direction a dry air flow develos. The quantity of vaour, leavin the roo by diffusion is very sall in coarison with that, leavin with the ventilation air. However vaour flow throuh buildin eleents has to be calculated in order to check the artial ressure distribution within the eleent and to revent the henoenon of interstitial condensation. It follows fro the above that vaour diffusion should be analyzed if there is a sinificant vaour ressure difference between the indoor sace and the environent, and there is a sinificant teerature difference, too. 22 t[ C ] In the ractice a steady state vaour flow is calculated. Considerin that the vaour diffusion is a very slow rocess, the ean teerature and the ean relative huidity of the outdoor air in the coldest winter-onth are taken as desin values.

13 Vaour transfer Vaour conductivity and resistance Vaour conductivity (δ) Siilarly to the heat flow, a vaour conductivity coefficient (or vaour diffusion coefficient) as a roerty of the aterial can be defined. The vaour conductivity is the vaour flow in tie unit at unit ressure difference between to oosite surfaces of a cube of unit size. The flow is durin the calculation considerd always one-diensional. The unit of the diffusion coefficient is usually: s MPa 2 s MPa Vaour resistance (R v ) The vaour resistance of a aterial is a easure of the aterial s reluctance to let water vaour ass throuh. The vaour resistance takes into account the aterial s thickness, so can only be quoted for a articular thickness of aterial. It is usually easured in MPa 2 /. R v b ( 2 s Ma ) Vaour resistance factor (μ) The µ-value of a aterial is also known as its water vaour resistance factor. It is a easure of the aterial s relative reluctance to let water vaour ass throuh, and is easured in coarison to the roerties of air. The µ-value is a roerty of the bulk aterial and needs to be ultilied by the aterial s thickness when used in a articular construction. Because the µ-value is a relative quantity, it is just exressed as a nuber (it has no units). R R v, at v, air ( ) Equivalent air layer thickness (s d ) You iht see the reluctance of a aterial to let water vaour ass throuh exressed as an equivalent air layer thickness, which is usually reresented as s d. As its nae suests, the equivalent air layer thickness is easured in eters. Like vaour resistance, it can only be quoted for a articular thickness of a aterial.

14 Vaour trasfer Overall vaour resistance of ultilayers Resistances bein additive, the resistance of a ultilayer eleent: R n n j R j j1 j1 j In the case of vaour transort the surface resistance is very sall, in ractical calculations it can be nelected. Thus, artial ressure at the surface is assued to be the sae as in the air in contact with the surface. R 0 R e 0 i b

15 Vaour transfer Overall vaour transfer Siilarly to the heat transfer distribution, the oisture transfer can be calculated on the basis of the balance condition: the flow enterin the syste equals with the flow leavin the syste. For ultilayer walls: i R e i e i e n n bj R j j1 j1 j i e artial water vaour ressure in the indoor air (Pa) artial water vaour ressure in the outdoor air (Pa) Vaour flux (/ 2,s) For any layer (because of the initial assution), the above equation can be alied also locally: R j j j ressure difference between the two boundary lanes of j-th layer Partial ressure values are to be calculated for the surfaces and lanes between two layers. Within one hooeneous layer the ressure distribution is linear. Now the desiner's task is to check whether the calculated artial ressure values are below the saturation values everywhere in the cross section.

16 i Calculation of oisture transfer Exale ti=20 C Rhi=65% Psi=2338Pa i=0,65*si=1520pa te=-2 C he=90% Pse=516a e=0,65*si=464pa internal convection b h W/K k W/ 2 K R 2 K/W T C d /s,ma Rd s,2,ma/ - 8 0,125 1,8 t iw =t i - t i = 18, ineral wool 0,05-0,057 0,877 12,3 t 12 =t iw - t 1 = 5,9 0,08 0, brick 0,30-0,577 0,520 7,3 t 23 =t 12 - t 2 = -1,4 0,05 6, e external convection ,042 0,6 t e =t ew - t e -2, U=1/SuR q=(ti-te)/sur Teerature distribution SuR: 1,564 22,00 SuRd 6,625 0,639 W/ 2 K 14,1 W/ 2 =(i-e)/surd: 159,40 P Pa Distr. Part. Press Exale1: Calculate the artial ressure dsitribution of a two layer wall! Heat calculation: R i =1/h i ; R 1 =b 1 /k 1 ; R 2 =b 2 /k 2 ; R e =1/h e R= R i + R 1 + R 2 + R e q=(t i -t e )/ R t I =q R I ; t 1 =q R 1 ; t 2 =q R 2 ; t e =q R e Checkin: t=t i -t e Partial ressure calculation: R d1 =b 1 /d 1 ; R d2 =b 2 /d 2 R d = R 1 + R 2 i = si RH i; ; e = se RH e =( i - e )/ R d I =0; 1 = R d1 ; 2 = R d2 ; e =0; t iw =t i -dt i ; iw = i t 1,2 =t iw -dt 1 ; 1,2 = iw -d 1 t ew =t 1,2 -dt 2 =t i +dt i ; ew = 1,2 -d 2 = e

17 Modified ressure distribution curve

18 Vaour transfer Desin consideration The risk of condensation is the hihest in the outside half of the theral insulation layers. Theral insulation aterials have hih resistance aainst heat flow (->bi teerature dro), but their resistance aainst vaour flow is usually sall. The oosite relates to the aterials of load-bearin and outside surface coatins layers. This is, why calculated artial ressure is near to the saturation value in the outside half of the theral insulation layer: the teerature is low, the artial ressure is hih. The risk can be revented and condensation can - theral insulation is outside (the whole cross section is ket war, the only roble is the resistance of the outside surface coatin) - there is a slihtly ventilated air a between the outside surface coatin and the theral insulation - in this air a the artial ressure is ractically the sae as in the outdoor air, if the thickness of the air a is in. 2 c and it is really vented there is a vaour retarder in the construction (a fil - like very thin layer.. lastic follies) havin bi resistance.