PREDICTING HUMAN GEOMETRY-RELATED FACTORS FOR DETAILED RADIATION ANALYSIS IN INDOOR SPACES

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Eghth Intenatonal IBPSA Confeence Endhoven, Nethelands August 11-14, 003 PREDICTING HUMAN GEOMETRY-RELATED FACTORS FOR DETAILED RADIATION ANALYSIS IN INDOOR SPACES K. Kuaha, D. Fala and K. J.

1 Eghth Intenatonal IBPSA Confeence Endhoven, Nethelands August 11-14, 003 PREDICTING HUMAN GEOMETRY-RELATED FACTORS FOR DETAILED RADIATION ANALYSIS IN INDOOR SPACES K. Kuaha, D. Fala and K. J. Lomas Insttute of Enegy and Sustanale Development (IESD, De Montfot Unvesty, Scaptoft Campus, Leceste, UK ABSTRACT In ths study, fomulae fo pedctng pojected aea factos and vew factos of ndvdual ody pats of standng and sedentay humans fo detaled adaton analyss wee developed. Fo ths pupose, detaled geomety models of the human ody wee geneated epesentng an aveage suject th a heght of 1.75 m and a DuBos aea of 1.83 m. Themal analyss softwae ncopoatng advanced, voxel-ased ay tacng technques and egesson analyss wee deployed to model the local pojected aea factos of humans exposed to dect and dffuse sola adaton. A method was developed to pedct vew factos of ndvdual ody pats ased on the pojected aea facto calculatons. Ths technque makes t possle to pedct vew factos etween ndvdual ody pats and suoundng sufaces fo almost any atay geometcal confguatons of the adaton envelope. The pedcted vew factos wee valdated and showed good ageement th expemental data avalale n the lteatue. INTRODUCTION Radatve heat exchange etween the human ody and the envonment plays an mpotant ole n the human heat tansfe and themal comfot. In uldngs, humans ae fequently exposed to nhomogeneous adaton that causes occupants dscomfot e.g. n close poxmty of cold ndows, hot adatos, etc. Moeove, asymmetc adaton due to non-unfom suface tempeatues, dect sola adaton o othe hgh ntensty atfcal souces causes local dscomfot at ndvdual ody pats and makes occuped zones uncomfotale. Themal dscomfot causes estctons n the usalty and functonalty of spaces, and educes occupants pefomance at the wokplace. The alty to pedct the nhomogeneous human adatve heat exchange also has enefts fo assessng wok effcency, safety and health. Two dffeent geomety factos ae needed to pedct the human adatve heat exchange. Pojected aea factos (f p ae needed to pedct the shot-wave adaton, whle vew factos (φ etween the human ody and sufaces of the enclosue ae equed when pedctng the long-wave adatve heat exchange etween humans and the suoundngs. Both factos have een sujected to vaous expemental nvestgatons n lteatue ut the esults ae avalale only fo the whole ody. They ae not avalale fo ndvdual ody pats equed fo detaled human adaton analyss. Fotunately, n ecent yeas, sophstcated compute smulaton softwae and themal analyss tools have emeged whch make detaled modellng and pedcton of the human adatve heat exchange n uldngs possle e.g. RadThem (RadThem, 001, Pose4 (Pose4, 000, ESP- (Clak and McLean, 1988, and dvese CFD package (CFX-5, 00. Such softwae s capale of dealng th hghly complex geometes such as the human ody (Fgue 1 and pedctons compae well th expemental measuements, Cuan A.R. et al. (1995, Lomas et al. (1994 and Cook, M. J. and Lomas K. J. (1998. Futhemoe mult-node models of the human themal system e.g. Stoljk (1970 and Fala (1999, 001 have een developed as thee s a gong need to pedct human physologcal and themal comfot esponses n vaous dscplnes of scence and technology. Also these models have een shown to epoduce well th n expemental esults, Fala (001, 003. The am of ths study s to develop fomulae and technques fo calculatng human pojected aea factos and vew factos fo ndvdual ody pats of the human ody. The new fomulae and calculaton technques developed n ths study can e used n conjuncton e.g. th mult-segmental models of the human tempeatue egulaton and themal comfot. As an exampale the IESD-Fala mult-segmental dynamc model was used to ncopoate the fomulae and technques to pedct human esponses to themally asymmetc envonments. The smulaton esults ae compaed th expemental data n ths pape. METHODOLOGY Human ody models The human ody, oth standng and sedentay, was modelled as havng left-ght symmety and a stessfee poston usng the Pose4 softwae (Pose4,

000. The softwae s capale of geneatng detaled 3D models of the human ody at almost any atay postue. The models conssted of 10995 small suface Tale 1. Aea of ndvdual ody pats of the human ody model.

2 000. The softwae s capale of geneatng detaled 3D models of the human ody at almost any atay postue. The models conssted of small suface Tale 1. Aea of ndvdual ody pats of the human ody model. No. Body pats Body sectos 1 Head Head Foehead Face Anteo Left & ght 3 Neck Anteo L.& R. Exteo Posteo 4 Shoulde Left Rght 5 Thoax Anteo L. & R. Infeo Posteo 6 Adomen Anteo L. & R. Infeo Posteo 7 Uppe ams Anteo Exteo Infeo Posteo 8 Lowe ams Anteo Exteo Infeo Posteo 9 Hands Handack Palm 10 Uppe legs Anteo Exteo Infeo Posteo 11 Lowe legs Anteo Exteo Infeo Posteo 1 Feet Instep Sole Suface Aea [m ] Fgue 1. The human ody geomety models used n the study. exteo elements to povde suffcent detal fo the adaton smulatons (Fgue 1. The elements wee gouped togethe nto 59 man ody pats (Tale 1 and spatal sectos (Fgue epesentng an aveage male th a heght of 1.75m and a DuBos aea of 1.83 m. Smulaton stategy The humanod geometes wee mpoted nto the themal analyss softwae package (RadThem, 001 whch uses a voxel-ased ay tacng technque to pedct the asoed shot-wave adaton enegy at each of the suface elements. At ths stage the suface elements wee defned as lack ody adatos th an asoptvty of one. Gven the ncdent flux, the asoed adaton of each suface element was calculated y the softwae. The esults wee then postpocessed ntegatng the elemental fluxes to otan pojected aea factos fo ndvdual ody sectos (face, foehead etc.. The total amount of sola adaton asoed y a ody secto consstng of n suface elements was otaned as the sum of pedcted nodal quanttes, Q a,. Fo a goup of ody nodes, the pojected aea facto, f p, s thus pesented as: f p anteo posteo 1 q s nfeo n 1 n 1 Q font ack Fgue. Sudvson of ody pats nto spatal sectos. a, A Body (1 whee f p = pojected aea facto of a ody secto; [-] Q a, = sola adaton asoed y suface element, ; [W] q s = ncdent sola adaton flux; [W/m ] A = aea of suface element,. [m ] Modellng pojected aea factos The pojected aea factos wee modelled fo oth dect and dffuse shot-wave adaton. They wee consdeed as a functon of the azmuth angle,, and alttude angle,, fo the case of dect shot-wave adaton. The angles wee ncluded fo all sphecal postons of the sun, hence, vaed fom 0 to 360 (due noth, clockse and vaed fom 90 to 90. Fo the dffuse shot-wave adaton case the pojected aea factos wee consdeed as a functon

3 of the gound eflectance, ρ, whch was vaed etween 0 and 1 whle assumng an sotopc sky. Smple and polynomal egessons wee used to deve the coeffcents of the pojected aea facto equatons. If any egesson coeffcent was not sgnfcantly dffeent fom zeo at the 0.95 confdence level, a new egesson was un thout the non-sgnfcant vaale. The two-taled populaton t-test was appled to detemne the sgnfcance level of the egesson coeffcents. Fo dect shot-wave adaton and most ody sectos (such as anteo, posteo and some exteo ody sectos the pojected aea facto cuves could e desced as peodc cosne functons of the azmuth angle,. Howeve, the functons wee not epoduced well fo some ody sectos that wee hdden o shaded y othe ody pats such as the nfeo ody sectos. Fo these, t was necessay to account fo the shadng effect y devng a so called shadng-functon as a pat of the fnal soluton fo each ody secto: whee and S f p S ( Acos( c1 c0 B (3 tanh( d1 d0 tanh( e1 e0 1. (4 In equaton (, Ω s the asc functon and S s the shadng functon of a ody secto. The coeffcents A, B, d 1, d 0 and e 1, e 0 as well as c 0 and c 1 wee detemned y egesson analyss. Each of these coeffcents wee functons of the alttude angle,. The egesson coeffcents A, B, d 1, d 0, e 1 and e 0 wee detemned usng polynomals of up to ode fou, whle c 0 and c 1 wee consdeed as coeffcents of lnea functons of. The pojected aea factos fo dffuse shot-wave adaton of ndvdual ody sectos wee modelled as lnea functons of the gound eflectance: f p c 1 c 0 (5 whee f p = pojected aea facto of a ody secto; [-] = gound eflectance; [-] c 0 and c 1 = egesson coeffcents of a ody secto. [-] Modellng vew factos Fo each suface secto of the human ody, A, and any atay plane of the adaton enclosue, A w, the vew facto s a functon of the elatve geometc elatonshps: 1 cos cos w w da da. (6, w A A A w Note that the tem cos da s the (dffeental pojected aea (da p of the ody secto, A. The coespondng pojected aea facto (df p s then the ato of da p and the coespondng actual aea. Equaton (6 can theefoe e expessed as a functon of the pojected aea facto, f p, whch, when ecast n numecal ntegaton fom, gves: 1 n m 1 w f A cos A (7, p j, j w j, A j11 j, whee φ,w = vew facto of the ody secto, A, th espect to plane, A w ; [-] j = unnng nume fo suface elements of the ody secto A ; [-] = unnng nume fo plane elements of the plane A w ; [-] j, = squae asolute of the dstance vecto f p j etween the ody element, j and the plane element, ; [m] = pojected aea facto of ody suface, j,, th espect to plane element, ; [-] = angle etween and the vecto nomal w j, to the plane element, ; [ad] A = aea of the plane element, ; [m ] A j = aea of the ody suface element, j; [m ] A = total aea of the ody secto. [m ] Intoducng the pojected aea factos, f p, fo a whole ody secto (equaton 1, assumng the cental coodnate (x, y, z s ts epesentatve coodnate, and the cental coodnate (x, y, z s the epesentatve coodnate of the plane element, (Fgue 3, then the vew facto of the ody secto th espect to the plane s w 1 m 1 1 f p cos A, (8 whee f p = pojected aea facto of the ody secto, A, th espect to the plane element, A ; [-] m = nume of suface elements of the plane, A w. [-] A (x, y, z n z x y Fgue 3. Geometc data nvolved n the calculaton of the vew facto etween a ody secto and a plane. A w A (x, y, z

4 The tem f p n equaton (8 depends on the azmuth angle, α, and the alttude angle,, accodng to equatons ( to (4. Hee α and etween the ody secto and a suface element of the wall s calculated y usng the follong equatons: ( y y tan( (9 ( x x whch gves and tan( hence ( tan 1 y y (10 ( x x ( x x ( z ( y y z ( z z (11 1 ( z z tan. ( x x ( y y ( z z (1 The angle, β, etween and the nomal vecto, n, of the plane element,, s detemned y: whee n n = n n and n cos (13 n = nomal vecto of the plane element, x y z ; n x = = = ; n y = 1 ; n z = x y z x x = y y z z x y z (14 (15. (16 RESULTS AND DISCUSSION Vefcaton Fo vefcaton puposes, the pedcton of pojected aea factos and vew factos fo each ndvdual ody secto of the standng and sedentay human, wee ntally compaed th the esults otaned y the voxel-ased ay tacng technque, (RadThem, 001. As examples, the pojected aea factos of the ght face exteo and foehead of a standng and sedentay peson ae llustated, fo dect shot-wave adaton n Fgue 4, and fo dffuse shot-wave adaton n Fgue 5. Pojected aea facto [-] Pojected aea facto [-] The pedctons fom the egesson equatons (sold lnes ae n good ageement th the pedctons (data ponts acoss the complete ange of azmuth (α and alttude ( angles. As can e seen, also the shadng functon accounted appopately fo the shadong effects y othe ody pats (e.g. at = -60, etween 40 <α<160 fo ght face exteo and at =-60, etween 10 <α<40 and 30 <α<350 fo foehead, Fgue 4. Pojected aea facto [-] Fgue 4. Pojected aea facto cuves fo dect shot-wave adaton of two ody sectos Gound Reflectance [-] Gound Reflectance [-] RadThem Azmuth angle a Standng postue egs. Rght face exteo Azmuth angle Sedentay postue Rght face exteo Foehead Foehead RadThem egs. egs. egs. a Standng postue Sedentay postue Fgue 5. Pojected aea facto cuves fo dffuse shot-wave adaton of two ody sectos

5 Fo dffuse shot-wave adaton (Fgue 5 the egesson equatons povded a vey good ft to the f p -factos fo all ody sectos and clealy pefomed as lnea equaton th coelaton coeffcents close to unty. As an example, the vew factos of the left am (lowe exteo pat and anteo thoax th espect to a font wall fo oth standng and sedentay postues ae shown n Fgue 6. Sold lnes epesent pedcted vew factos usng equaton (8, the data ponts epesent the esults otaned y the voxelased ay tacng technque. The pedctons and the smulated esults wee compaed y vayng the dmensonless values a/c and etween 0. and 10 (see Fgue 7 fo geometc confguaton. As can e seen, the pedctons wee n good ageement th the RadThem values Left am: lowe exteo a Standng postue (c=10.0 m. Thoax: anteo Sedentay postue (c=5.0 m. Fgue 6. Vew factos etween ody sectos and a wall n font of a peson. a/c = 0. a/c = 0.4 a/c = 0.8 a/c = 1. a/c =.0 a/c = 3.0 a/c = 4.0 a/c = 6.0 a/c = 8.0 a/c = 10.0 egs. a/c = 0. a/c =.0 a/c = 10.0 egs. Valdaton To date, most expemental data s avalale just fo the whole ody. Theefoe, the pedcted esults otaned fo ndvdual ody sectos wee ntegated ove the whole ody and wee compaed th expemental esults povded y Fange (1970 and Hokosh et al. (1996. Theey, the vew factos of ndvdual ody sectos wee pedcted th espect to fou geometc confguatons: font wall (FW, sdewall (SW, celng (CE, and floo (FL, Fgue 7. Fo valdaton puposes the geomety was set up to match the expements of Fange n ths study. The esults desced n ths pape ae howeve equally vald fo any atay enclosue. The vew factos wee calculated y vayng the dmensonless dstances a/c and. Hee, a and ae the length and heght of a plane and c s dstance etween the cente of the ody and the plane c 1.0m Fange Hokosh: a/c=1.0 Hokosh: a/c=1.5 Hokosh: a/c=.0 SW c CE FL Regs. FW a 1.0m. Fgue 7. Geometc confguaton of the enclosue used n the valdaton wok. a Font wall Fgue 8. Vew factos etween the whole ody and planes n font of a standng peson. a/c =.0 a/c =

6 0.1 Sdewall a/c = a/c = Fange Hokosh: a/c=1.0 Hokosh: a/c=1.5 Hokosh: a/c=.0 Regs. 0.1 c Celng a/c = a/c = Fange Hokosh: a/c =1.0 Regs. 0.1 d Floo ageement etween the pedctons (sold lnes and expemental values fo most a/c and values. An excepton fom pedcted vew factos to the floo whch ae geate than n the expements of Fange ut lowe than the expemental esults of Hokosh. Some easons fo the dscepances etween pedctons and measuements ae: a. the human ody smulated could dffe n geomety fom the sujects n the expements and. thee would e dffeences etween postues smulated and the standng and sedentay postues adopted y expemental sujects. Futhe compasons of vew factos fo the sedentay postue ae shown n the Appendx. As a fnal expemental valdaton, and to llustate the value of the lnk etween the mult-node dynamc IESD-Fala comfot model and the adaton model, the skn tempeatues, ectal tempeatue and sweatng ates wee pedcted n extemely asymmetc adant envonments. The esults wee compaed aganst expemental data otaned y Hall and Klemm (1969. In the expements the human ody was lad down supne on a net n the cente of a chame whch was dvded nto an uppe and lowe secton. Fve expements wee conducted th the wall tempeatues of the uppe half and the lowe half set at 104 C and 6.7 C, 93 C and 6.7 C, 8 C and 6.7 C, 65 C and 11.0 C and 53 C and 11.0 C, espectvely (expement 1,, 3, 4 and 5. The a velocty, aveage a tempeatue and wate vapou pessue n the chame wee m/s, 0 C and.5 mmhg, espectvely. The sujects wee clad only n undewea (I cl =0.3 clo. 45 Aveage anteo skn tempeatue 0.0 a/c =.0 a/c = 0. Skn tempeatue [C] Fange Hokosh: a/c =1.0 Hokosh: a/c =1.5 Hokosh: a/c =.0 Fgue 8. (Contnued. Regs. The pedctons wee pefomed y settng a/c and at 0., 1.0, 1.5,.0 and 5.0. The dstance, c, etween the ody and the walls (font wall and sdewall was set at 1.0 m and the celng aove the floo was 3.0 m. It can e seen that thee s a good 5 Aveage posteo skn tempeatue a Skn tempeatue Exposue tme [mn] Exp 1 Exp Exp 3 Exp 4 Exp 5 Sm. Fgue 9. Compason of the smulaton and expemental esults fo a human ody n asymmetc adant envonments

7 Tempeatue [C] Sweatng ate [g/mn] Exposue tme [mn] Exp1 Exp Exp3 Exp4 Exp5 Rectal temp. 1 Rectal temp. Rectal temp. 3 Rectal temp. 4 Rectal temp. 5 Sm. Aveage skn tempeatue and ectal tempeatue c Sweatng ate Fgue 9. (Contnued. Rectal tempeatue Aveage skn tempeatue Mean skn tempeatue [C] Exp Sm The skn tempeatues of ndvdual ody sectos wee pedcted and aveaged ove the anteo and posteo ody pats and the whole ody accodng to the expemental potocol. Geneally, the smulatons ageed well th the expements fo oth anteo skn tempeatues and posteo skn tempeatues (Fgue 9a. An excepton fomed expement 1, fo whch the dscepancy etween expement and pedcton was geate than the expected expemental eo (ndcated as as n Fgue 9a. Also the sweatng ates and the ody coe (ectal tempeatue pedctons wee n good ageement th the expemental data (Fgue 9 and 9c. CONCLUSION The pedcted pojected aea factos and vew factos developed hee showed good ageement th expemental esults otaned y Fange (1970 and Hokosh et al. (1996. To llustate the use of the developed equatons the new adaton model was ncopoated n an exstng mult-segmental dynamc model of human tempeatue egulaton and themal comfot, Fala et al. (1999, 001, 003. The pedctons poduced good geneal ageement th expemental data oseved n asymmetc adant envonments. Scentsts and engnee can use the pojected aea factos and vew factos to pefom detaled adaton fo uldng occupants. Togethe th a themal comfot model these factos ll assst achtects, desgnes, uldng smulaton vendos, and eseaches to quantfy the comfot pefomance of uldngs and HVAC systems, as well as ndvdual ult constuctons such as ndows, heated floo, adatos and etc. The comned model ll also have value n analysng the health and safety ctcal themal envonments. REFERENCES CFX-5 (00. Solve and solve Manage: Radaton n CFX-5, CFX Intenatonal, AEA Technology plc. Ddcot, UK, Release 00. Clak J.P. and D. McLean. (1988. ESP A uldng and plant enegy smulaton system. Veson 6, elease 8, Enegy smulaton Reseach Unt, Unvesty of Stathclyde and ABACUS Smulatons Ltd., Glasgow, UK. Cook, M. J. and Lomas K. J. (1998. Buoyancydven dsplacement ventlaton flows: Evaluaton of two eddy vscosty tuulence models fo pedc-ton. Buldng Sevces Engneeng Reseach and Technology, vol. 19, no. 1, pp. 15-1, Cuan A.R. et al. (1995. Automated adaton modelng fo vehcle themal management, 1995 SAE Intenatonal Congess and Exposton, Coo Cente, Detot, USA, Mach, Fange, P.O. (1970, Themal Comfot - Analyss and Applcatons n Envonmental Engneeng, Techncal Unvesty of Denmak, Laoatoy of Heatng and A Condtonng, McGaw-Hll Book Company Fala D., K.J. Lomas and M. Stohe. (1999. A compute model of human themoegulaton fo a de ange of envonmental condtons: the passve system. The Amecan Physologcal Socety, Vol. 87(5, pp Fala D., K.J. Lomas and M. Stohe (001. Compute pedcton of human themoegulatoy and tempeatue esponses to a de ange of

8 envonmental condtons. Intenatonal Jounal of Bometeoology, Volume 45 (001, pp Fala D., K.J. Lomas and M. Stohe (003. Fst pncples modellng of themal sensaton esponses n steady state and tansent condtons. ASHRAE Tansactons, volume 109, pp Hall J.F. J., and F.K. Klemm (1969. Themal comfot n dspaate themal envonments. Jounal of Appled Physology, Vol.7, No.5, pp Hokosh T. et al. (1996, The effectve adaton aea and angle facto etween man and a ectangula plane nea hm. ASHRAE Tansacton, volume 90, 1996, pp Lomas K.J., H. Eppel, C. Matn, and D. Bloomfeld. (1994. Empcal valdaton of themal uldng smulaton pogams usng Test Room data. IEA, Enegy consevaton n uldngs and communty systems pogamme. Annex 1: Calculaton of enegy and envonmental pefomance of uldngs and sola heatng and coolng pogamme. Task 1: Buldng enegy analyss and desgn tools fo sola applcatons: Vol. 1, Fnal Repot, 141-pp., Vol.. Empcal Valdaton Package, 78-pp., Vol. 3, Wokng Repot, 94-pp., Pose4. (000, POSER4, The Peme 3D Chaacte Anmaton and Fgue Desgn Tool, Use Gude fo Macntosh and Wndows, Cuous Las, Inc. RadThem (001, RadThem Techncal Documentaton, Daft, (updated though veson 6.0. ThemoAnalytcs, Inc. Stoljk J.A.J. (1970. Mathematcal model of themoegulaton, Physologcal and ehavoual tempeatue egulaton, chapte 48, Chales C. Thomas Pu., pp APPENDIX a Font wall Fange Hokosh: a/c=0.5 Hokosh: a/c=1.0 Hokosh: a/c=.0 Regs. a/c =.0 a/c = Sdewall Fange Hokosh: a/c=0.5 Hokosh: a/c=1.0 Hokosh: a/c=.0 c Celng Regs a/c =.0 a/c = 0. a/c =.0 a/c = 0. Fange Hokosh: a/c =0.5 Hokosh: a/c =1.0 Regs. d Floo a/c =.0 a/c = 0. Fange Hokosh: a/c =1.0 Hokosh: a/c =.0 Regs. Fgue 10. Compason of pedcted and measued vew factos etween a sedentay human ody and suoundng planes at dffeent dstances

FUNDAMENTALS OF RADIOMETRY

1 FUNDAMENTALS OF RADIOMETRY Lectue 5 Radomety 2 Quanttatve measuement of the popetes of EM adaton nteacton wth matte o emsson fom t Radomety deals wth total EM adaton We extend the concept of adans n