Model and program for the prediction of the indoor air temperature and the indoor air relative humidity

Transcription

1 Insttute of Buldng Clmatology, Faculty of Archtecture, Dresden Unversty of Technology, Germany Model and program for the predcton of the ndoor ar temperature and the ndoor ar relatve humdty Dr.-Ing. A. Bshara & Prof. Dr.-Ing. habl. (em.) P. Häupl Dresden Unversty of Technology, Germany Dpl. Ing. (FH) F. Hansel Unversty of Technology Cottbus Senftenberg, Germany Venna 10/09/2013

2 Outlook - Introducton and boundary condtons - Modelng of energy balance - Modelng of mosture balance - Results and concluson

3 Test house constructon wth outdoor clmate loadng, mosture sources ndoor heat and gven usng regme Drect / dffuse radaton Outsde ar temperature outdoor ar humdty External buldng part : roof tendency 0, 30, 45, 60, 90 ventlaton Wndow wth varable shadng Room ar temperature Room ar humdty Insde buldng part: celng, floor Room 3 Internal heat and mosture sources Room 1 ventlaton Wndow wth fxed foregn shadng Insde buldng part: Wall Insde buldng part: Door Room 4 Room 2 Heatng External buldng part: wall poston north, northeast, East, Southeast, South, Southwest, West, Northwest

4 Outdoor clmate (measured values, Dresden 1997) column 1- Temperature Apr 11th column 2- Relatve humdty column 3- Drekt radaton column 4- Dffuse radaton column 5- Precptaton KU2 = column 6- Wnd velcty column 7- Wnd drecton Apr 12th

5 Modellng of the energy balance 1 th Energy balance of the outer surface dθoe SW = T ' W.( θoe θo ) + Ü e.( θoe θe ) + C e. dt 2 nd Energy balance of the ndoor ar Φ = Ü e. ( θ oe θ ) Ü e e θ oe θ e Φ = a.g a Φ TW = T W. ( θ Oe θ O ) SWe θ oe C e d Φ SPe = C e. θ dt Oe θ θ oe 0 = ( L + T ).( θ θ ) + Ü.( θ θ ) + F e o J 2 Φ TW = T W ( θ oe θ o ) Φ = S θ oe SF Φ = Ü ( θ o θ ) Ü. θ o θ F J Φ = 2 θ o d Φ S P = C. θ dt o C θ o d Φ S P = C. θ d t o θ o C 3 rd Energy balance of the nner surface Φ = ( θ o θ ) Ü. Ü dθo J C. = SF + T ' W.( θoe θo ) + Ü.( θo θ ) + dt 2 θ e Φ L = L. ( θ e θ ) Φ TF = T F. ( θ e θ ) θ o θ θ J Φ = 2 d Φ S p L = C L. θ C d t L

6 Indoor ar temperature for the tme step +1 =1, θ, + 1 = θ, + ( θlim, θ, ).( 1 exp( β. t )) Lmt temperature for each tme step θ LIM, S S S F F W Üe T ' W Üe Üe T ' W J Ü.. 1 J ( L ( L + T F ) + T F ) 2 L TF Ü = θ e, L + Ü + T Ü T ' Ü L + T Ü T ' Ü L + T e W F e W F F Tme coeffcent E E β = + B τ = 3 β T ' W + Üe = 1 1 B +. C.C e Ü L TF T ' W Üe Ü 1 T ' W + Üe T ' W + Ü E =. C ( + ). L T 1 1 F + Ce C + Ü L TF

7 Modellng of the mosture balance Example: Readng room of the lbrary wth hgh heat and mosture capacty p C F p d d m = C. p dt dt SPL LF d C. p = Ü. p p dt ( ) F O F O d m = Ü. p p Ü dt ( ) F O p o θ e C LF p p p p e se s θ C F p o φ e φ d V L.n L pe p m L = dt R D T e T d m = m.v dt QU ptv L

8 Modellng of the mosture balance 1 th Mosture balance of the outer surface d m 0 T = dt 2 nd Mosture balance of the ndoor ar dp V.n p p ( ) L L e C LF. =. + Ü F. po p + m ptv.v L dt RD Te T dp C. = Ü. p p dt 3 rd Mosture balance of the nner surface ( ) o F F o 1 t δ w C =... ρ..a sp L h F W o 2 π µ ps

9 Vapor pressure on the nner surface for the tme step +1 =1, ( ) ( ) p = o, 1 p + o, p o,lim, p o,. 1 + exp( β F.t ) p o,lim, = p + e, m.r.t ptv D n L Heren means p o,lim,, the water vapor pressure at the surface after an nfntely long tme β F = 1 1. C R F D.T 1 + V.n Ü L L F b F s the tme constant for the humdty adustment wthn the -th tme step

10 Vapor pressure and relatve humdty of the room ar for the tme step +1 =1, Fnally we can determne the water vapor pressure of the room ar p, + 1 = V.n L L p o, + 1.Ü F + p o, R D.T V L.n L ÜF R D.T 17,26. θ, ,87. θ, ,3+, 265,5+ θ + 1, + 1 e. + e = θ p (, 1 ) s, 1 610,5. Φ θ (, 1 10 Φ θ + ) The nsde relatve humdty at the tme +1 s φ, + 1 = p p, + 1 s, + 1

11 Valdaton of the humdty module 100,00 80 temperature n C / relatve humdty n % 90,00 80,00 70,00 60,00 50,00 40,00 30,00 20,00 10,00 Ph flow nto Ph clmt Ph mes T m es temperature n C / relatve humdty n % Ph flow nto Ph clmt Ph mes T mes 0, tm e n h Comparson between measured and calculated relatve humdty n the empty box tme n h Comparson between measured and calculated relatve humdty n the box wth the sample wooden concrete: mosture ump 65%/45%, ump tme 24h, ventlaton rate 0.4/h Test box wth wooden concrete samples and measurement equpment

12 Example 1: Readng room of the lbrary wth hgh heat and mosture capacty Yearly course of the ndoor ar temperature outdoor ar temperature (Dresden) n comparson 35 Outdoor/Indoor Außenluft/Raumlufttemperatur ar temperature C C θ ( ) T Zet n 4h Tme n days

13 Example 1: Readng room of the lbrary wth hgh heat and mosture capacty Yearly course of the ndoor relatve humdty outdoor ar relatve humdty (Dresden) n comparson Indoor Relatve ar Luftfeuchgketen relatve humdty n 1 n 1 KD ( ) 100 φ, m ptv t( ) Zet n Tagen Tme n days

14 Program CLIMT (Clmate-Indoor-Mosture-Temperature) Input data for the room parameters

15 Example 2: Archve room of the lbrary Magdeburg wth hgh heat and mosture capacty Tm n day

16 Example 2: Archve room of the lbrary Magdeburg wth hgh heat and mosture capacty Comparson between measurement and calculaton (clmate Magdeburg 2012) by CLIMT Indoor ar relatve humdty Indoor ar temperature

17 Example 3: Swmmng house n South Brandenburg

18 Example 3: Swmmng house n South Brandenburg Indoor ar temperature n the swmmng house n 2008: Calculated by TRNSYS (ponted magenda lne), calculated by CLIMT (black lne) and measured values (cyan lne) Indoor ar temperature n C θpb( ) θp( ) θt( ) Tme n d

19 Example 3: Swmmng house n South Brandenburg Indoor ar relatve humdty n the swmmng house n 2008: calculated by CLIMT (black lne) and measured values (green lne) Indoor ar relatve humdty n % φpb( ) φp( ) Tme n d

20 Summary - The model and also the program CLIMT for the practcable calculaton of the ndoor ar temperature and relatve humdty has been developed - The results have been compared for a test box and for two actual test houses. All results correspond very good

21 Thank you for your attenton