CONTINUOUS_MODEL CeWind ABSTRACT "WINDow, internal shading controlled by schedule or heat flux. Use of shading factors (for background, cf ASHRAE Fundamentals, pp 27.14-19): SF Solar Factor Solar heat gain / Incident solar also called SHGC Solar heat gain coefficient SC Shading coefficient SF(current) / SF(reference) SSC Shortwave shading coefficient Direct energy transmission / SF for reference The reference is single-pane, double-strength clear glass. The SF of this glass is 0.87 for normal incidence. Other references are used locally; in Sweden mostly double pane insulating glass with SF 0.76. !?? More on angle dependance and split of absorbed between in & out. Internal shading is variable between states 0 & 1. Old version Time control Shading is ON between given times. Solar control Shading is ON, IF solar radiation / m2 exceeds 'ctrlLevel' AND incident angle is less than ctrlAngle. When both controls are selected, either condition suffices to turn shading on. New version Time control Variable 'SchedShading' has two modes: Continuous in (0,1) if solar control is OFF; 0 or 1 (< 0.5 <), if solar control is ON. Solar control Parameter 'solarCtrl' takes values 0 or 1. Combined action When solarCtrl = 1, shading is ON, IF solar radiation / m2 exceeds 'ctrlLevel' AND incident angle is less than ctrlAngle AND SchedShading > 0.5, otherwise OFF. When solarCtrl = 0, shading is proportional to SchedShading. End solar control The innermost and outermost pane temperatures are modelled. In the heat balance of the outermost pane is included longwave radiation from sky and ground and external covection w variable convective heat transfer coefficient. It is assumed that total h-values supplied as parameters have been calculated with internal and external resistances adding up to 0.17 (m2 K)/W. History (in reverse order): 010226 ABg 'solar/transm': Combine direct and indirect solar vs pure transmission. Approximate scheme window outer inside pane | | <--- RDiffThru - - - - - - - - - - - - - - - <--- RDirThru - - - - - - - - - - - - - - - ---> RBack | | | | | <- - - - - - - - - - - - QAbsorb | | | | | | | <--- QGlassTransm - | | || <--- QFrameTransm - || || || 000717 AB Split diffuse into sky and ground. 000301 AB Modified shading control: continuous when solarCtrl OFF, ON/OFF otherwise. 000125 AB RBack is Radiation [W] but was multiplied by Area in calc of RBackThru. Factors for back radiation changed. 990519 MV A new link towards ambient. A new link type introduced as well. Back radition (RBackThru) through the window is calculated and total reflected SW radiation (QSWOut). LW radiation between outermost pane/frame and sky + ground is calculated into Wind2amb link. Back coming radiation is contributing to absorbed radiation even if the factors are NOT exactly correct for radiation from inside to ambient. 980908 PG Fixed default values for SC, SSC, SC_0, SSC_0 and RThruRef. 980831 AB Switch to single pane reference according to international use. 980503 PS Limits and defaults AngleInc and FThruDir 980430 PS High Limits for F1 and F2 980206 AB Solar ctrl by radiation inside panes. Exchanged RDirThru & RDiffThru. ................................................................... Ditto in forward order Control functions added 951115 by MV Modified dec 95 by AB 970417 MV Temperature control removed 970527 MV Parameters FrameRat, hFrame, absFrame and emitFrame are added to model frame part of window. The zone model sees only one temperature from window. Heat balance of frame is added. 970601 PS Change in shading control, so that load control is active only when time control is also active. 970613 AB Radiation on links is now CROSS 970922 AB Changed unit of F-factors from % to 1 971001 MV Link order is reordered according to face model 971002 AB Type of h_0 changed to HeatCondA " EQUATIONS /* Model for two pane reference window has been adjusted for ratio between SF(single)/SF(double) = 0.87/0.76 = 1.15. For diffuse radiation, double pane has been modelled to transmit 0.67 and single pane transmittance is here set to 1.15*0.67=0.77 */ IDiffInc := IDifSkyInc + IDifGrdInc; CosInc := cos(AngleInc*Pi/180); /* For normal incidence, FThruDir = ICE CEN triple pane 0.67 double pane 0.789 0.76 single pane 0.907 0.87 zero pane 1.0 1.0 */ FThruDir:= 1.15 * IF (AngleInc > 85) and (AngleInc <= 90) THEN 1.48*CosInc ELSE_IF (AngleInc > 75) and (AngleInc <= 85) THEN 1.8*CosInc-0.028 ELSE_IF (AngleInc > 0) and (AngleInc <= 75) THEN -0.105+CosInc*(2.821+ CosInc*(-2.998+CosInc*1.071)) ELSE 0 END_IF; RThruRef:= (FThruDir * IDirInc * AGlass + 0.77 * IDiffInc * AGlass); /* Intensity thru current glass type */ RThruCurrA := SSC_0 * ( FThruDir * IDirInc + + 0.77 * IDiffInc ); /* Shading controls, old version */ /* ShadingOn := IF schedShading > 0.5 */ /* on, if shedule and solar control */ /* AND solarCtrl > 0.5 */ /* AND AngleInc < ctrlAngle */ /* AND RthruCurrA >= ctrlLevel THEN */ /* 1 */ /* ELSE_IF schedShading > 0.5 */ /* or on, if shedule and no solar control*/ /* AND solarCtrl < 0.5 THEN */ /* 1 */ /* ELSE */ /* 0 */ /* END_IF; */ /* pick up the right factors */ /* IF ShadingOn > 0.5 THEN */ /* SC := SC_1; */ /* SSC := SSC_1; */ /* hPanes := 1 / (1/h_1 - 0.17); */ /* ELSE */ /* SC := SC_0; */ /* SSC := SSC_0; */ /* hPanes := 1 / (1/h_0 - 0.17); */ /* END_IF; */ /* Shading controls, new version */ ShadingOn := IF solarCtrl > 0.5 THEN /* on, if shedule and solar control*/ IF SchedShading > 0.5 AND AngleInc < ctrlAngle AND RthruCurrA >= ctrlLevel THEN 1 ELSE 0 END_IF ELSE /* or continuous, proportional to shedule, if no solar control*/ SchedShading END_IF; /* weigh together the two factors */ SC := SC_1 * ShadingOn + SC_0 * (1 - ShadingOn); SSC := SSC_1 * ShadingOn + SSC_0 * (1 - ShadingOn); hPanes := 1 / (1/h_1 - 0.17) * ShadingOn + 1 / (1/h_0 - 0.17) * (1 - ShadingOn); /* Heat transmision from outer pane */ QGlassTransm := AGlass * hPanes * (TWindOut - TIn); /* Heat transmision from outer frame */ QFrameTransm := AFrame * h_FramePure * (TFrameOut - TIn); /* Radiation transmitted */ /* Divide between direct and diffuse; */ /* currently, zone model handles all radiation as diffuse, except in calculation of lighting */ RDirThru = SSC * FThruDir * IDirInc * AGlass; RDiffThru = SSC * 0.77 * IDiffInc * AGlass; /* Absorbed heat */ /* From ambient and room */ QAbsFrOut := IF ShadingOn > 0.5 THEN 1 / (1 - h_1*0.11) ELSE 1 / (1 - h_0*0.11) END_IF * (SC-SSC) * RThruRef; QAbsorb := QAbsFrOut + RBack * (SC - SSC) / SC; /* Heat balance of innermost pane */ QGlassInside := - QAbsorb - QGlassTransm; /* Heat balance of inner frame */ QFrameInside := - QFrameTransm; QInside = QGlassInside + QFrameInside; /* LW radiation */ QLWOutPane := (1+cos(slopeWind*PI/180))/2 * emitWind * BOLTZ * AGlass * /* ((TSky-ABS_ZERO)**4-(TWindOut-ABS_ZERO)**4) */ ABS(((TSky-ABS_ZERO)**2+(TWindOut-ABS_ZERO)**2) * ((TSky-ABS_ZERO) +(TWindOut-ABS_ZERO) ))* (TSky-TWindOut) + (1-cos(slopeWind*PI/180))/2 * emitWind * BOLTZ * AGlass * /* ((TGround-ABS_ZERO)**4-(TWindOut-ABS_ZERO)**4); */ ABS(((TGround-ABS_ZERO)**2+(TWindOut-ABS_ZERO)**2) * ((TGround-ABS_ZERO) +(TWindOut-ABS_ZERO) ))* (TGround-TWindOut); QLWOutFrame := (1+cos(slopeWind*PI/180))/2 * emitFrame * BOLTZ * AFrame * /* ((TSky-ABS_ZERO)**4-(TFrameOut-ABS_ZERO)**4) */ ABS(((TSky-ABS_ZERO)**2+(TFrameOut-ABS_ZERO)**2) * ((TSky-ABS_ZERO) +(TFrameOut-ABS_ZERO) ))* (TSky-TFrameOut) + (1-cos(slopeWind*PI/180))/2 * emitFrame * BOLTZ * AFrame * /* ((TGround-ABS_ZERO)**4-(TFrameOut-ABS_ZERO)**4); */ ABS(((TGround-ABS_ZERO)**2+(TFrameOut-ABS_ZERO)**2) * ((TGround-ABS_ZERO) +(TFrameOut-ABS_ZERO) ))* (TGround-TFrameOut); QLWOut = QLwOutFrame + QLWOutPane; /* Convection */ QConvPane := hExt * AGlass * (TAmb - TWindOut); QConvFrame := hExt * AFrame * (TAmb - TFrameOut); QConvOut = QConvFrame + QConvPane; /* SW back to ambient */ RBackThru := SSC / SC * RBack; QSWOut = RBackThru + ((IDirInc + IDiffInc) * AGlass - RDirThru - RDiffThru - QAbsFrOut); /* Heat balance of outermost pane */ /* 0 = - QGlassTransm + QConvPane + QLWOut; */ 0 = - QGlassTransm + QConvPane + QLWOutPane; /* Heat balance of frame's outersurface */ 0 = - QFrameTransm + QConvFrame + QLWOutFrame + AbsFrame * AFrame * (IDiffInc + IDirInc); /* solar/transm + */ /* Solar radiation INTO building */ QSolar := RDiffThru + RDirThru - RBack + QAbsorb; /* Window transmission INTO building */ QTransm := QGlassTransm + QFrameTransm; /* solar/transm . */ LINKS /* type name variables... */ Face2Wind Outside TAmb, TGround, TSky, hExt, IDirInc, IDifSkyInc, IDifGrdInc, AzimutThru, ElevThru, AngleInc; Wind2Amb FluxOutside POS_IN QConvOut, POS_OUT QSWOut, POS_IN QLWOut; TQ TqInside TIn, POS_IN QInside; RRRWW RadInside POS_OUT RDiffThru, POS_OUT RDirThru, POS_IN RBack, AzimutThru, ElevThru; Z CtrlShading schedShading; VARIABLES /* type name role def min max description */ Factor SC LOC 0.87 SMALL 1.3 "factor SC" Factor SSC LOC 0.81 SMALL 1.3 "factor SSC" Factor hPanes LOC 3.1 SMALL 5.9 "U-value betw innermost and outermost panes" Angle AzimutThru IN 97 0 360 "sun's rel azimuth" Angle ElevThru IN 19 0 90 "sun's elevation" Angle AngleInc IN 45 0 90 "incident angle of direct radiation" Factor CosInc LOC "COS(incident angle)" Factor FThruDir LOC 0 0 1 "transmission factor, direct radiation" /* solar/transm + */ HeatFlux QSolar LOC 1 SMALL BIG "solar radiation gain for building " HeatFlux QTransm LOC 1 -BIG BIG "transmission gain for building " /* solar/transm . */ HeatFlux QAbsFrOut LOC 19 -BIG BIG "rad absorbed, innermost, fr outside" HeatFlux QAbsorb LOC 19 -BIG BIG "rad absorbed, innermost, fr both sides" HeatFlux QInside OUT 18 -BIG BIG "heat from zone, conv+LW" HeatFlux QGlassInside LOC 17 -BIG BIG "heat from zone, conv+LW, glass part" HeatFlux QFrameInside LOC 1 -BIG BIG "heat from zone, conv+LW, frame part" HeatFlux QGlassTransm LOC -36 -BIG BIG "heat outer to inner pane" HeatFlux QFrameTransm LOC -1 -BIG BIG "heat outer to inner frame" HeatFlux QLWOutPane LOC 0 -BIG BIG "lw rad between pane and ambient" HeatFlux QLWOutFrame LOC 0 -BIG BIG "lw rad between frame and ambient" HeatFlux QLWOut OUT 0 -BIG BIG "sum lw rad above" HeatFlux QConvPane LOC 0 -BIG BIG "conv between pane and ambient" HeatFlux QConvFrame LOC 0 -BIG BIG "conv between frame and ambient" HeatFlux QConvOut OUT 0 -BIG BIG "sum conv above " Radiation RBackThru LOC 0 -BIG BIG "back coming radition through window" HeatFlux QSWOut OUT 0 -BIG BIG "sum reflected total rad and back coming radiation" RadA IDifSkyInc IN 84 0 BIG "incident diffuse rad fr sky" RadA IDifGrdInc IN 84 0 BIG "incident diffuse rad fr ground" RadA IDiffInc LOC 84 0 BIG "total incident diffuse rad" RadA IDirInc IN 0 0 BIG "incident direct rad" Radiation RThruRef LOC 156 0 BIG "total rad thru ref wdw" RadiationA RThruCurrA LOC 136 0 BIG "specific rad thru curr wdw" Radiation RDiffThru OUT 108 0 BIG "diffuse rad passing thru" Radiation RDirThru OUT 0 0 BIG "direct rad passing thru" Radiation RBack IN 4 0. BIG "diffuse rad coming back" Factor ShadingOn LOC 0 0 1 "shading 0=OFF/1=ON" Factor schedShading IN 0 0 1 "time control 0=OFF/1=ON" Temp TAmb IN 20 ABS_ZERO BIG "ambient temp" Temp TIn IN 25 ABS_ZERO BIG "temp of window seen by zone combined frame and pane temp." Temp TWindOut OUT 21 ABS_ZERO BIG "temp of outermost pane" Temp TFrameOut OUT 23 ABS_ZERO BIG "temp of outer frame" Temp TGround IN 20 ABS_ZERO BIG "ground temp" Temp TSky IN 15 ABS_ZERO BIG "sky temp" HeatCondA hExt IN 13 0 BIG "external conv heat coeff" PARAMETERS /* type name role def min max description */ /* BRIS-like input data */ Factor SC_0 S_P 0.87 SMALL 1.12 "factor SC wo shading" Factor SSC_0 S_P 0.81 SMALL 1.09 "factor SSC wo shading" HeatCondA h_0 S_P 3.1 SMALL 5.9 "U-value wo shading" Factor m_SC S_P 0.5 SMALL 1 "reduction thru shading" Factor m_SSC S_P 0.3 SMALL 1 "reduction thru shading" Factor m_h S_P 0.9 SMALL 1 "reduction thru shading" Area a S_P 1 SMALL BIG "window area" Factor FrameRat S_P 0.1 SMALL 1 "Frame area / total window area" Factor h_frame S_P 2 SMALL BIG "Frame U-value" Factor absFrame S_P 0.6 SMALL 1 "Absorption of frame" Factor emitFrame S_P 0.6 SMALL 1 "Emissivity of frame" Factor emitWind S_P 0.9 SMALL 1 "Emissivity of wind pane" Angle slopeWind S_P 90 0 180 "Slope of window surf, 0 = hor downward 90 = vertical 180 = hor upward; note: face is different" /* shading controls */ Factor solarCtrl S_P 0 0 1 "solar control on or off" Angle ctrlAngle S_P 0 0 180 "max angle for solar ctrl" RadiationA ctrlLevel S_P 0 0 BIG "min rad [W/m2] for ctrl" /* calculated parameters */ Factor SC_1 C_P "factor SC w shading" Factor SSC_1 C_P "factor SSC w shading" Factor h_1 C_P "U-value w shading" Area AFrame C_P "Frame area" Area AGlass C_P "Glass area" Factor h_framepure C_P "U-value wo inter and outer resistances" PARAMETER_PROCESSING SC_1 := m_SC * SC_0; SSC_1 := m_SSC * SSC_0; h_1 := m_h * h_0; AFrame := FrameRat * A; AGlass:= A - AFrame; h_framepure := 1 / (1/h_frame - 0.17); END_MODEL