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Review of Numerical Modelling of Outdoor Thermal Comfort The 2005 World Sustainable Building Conference, 06-026 Tokyo, 27-29 September 2005 (SB05Tokyo) REVIEW OF NUMERICAL MODELLING OF OUTDOOR THERMAL COMFORT Leonardo Marques MONTEIRO1 1 Department of Technology, Faculty of Architecture and Urbanism of University of Sao Paulo, Sao Paulo, Brazil, [email protected] Keywords: thermal comfort, thermal stress, outdoors, numerical modelling, comfort indexes Summary Although most thermal comfort studies consider only the indoor conditions, there are significant researches concerning outdoors. Evaluating open areas requires the comprehension of additional factors, which are not taken into account in a typical indoor situation, bringing more complexity to the thermal analysis. This paper reviews the researches in outdoor thermal comfort, specifically the numerical models proposed by several authors through thermal balance methodology and empirical researches. The first experiences made are illustrated by the empirical work of Houghten (1923), Vernon & Warner (1932), McAriel (1947) and Missenard (1948), originally published as nomograms. The equations and parameters of the former following empirical works are presented: Siple & Passel (1945), Belding & Hatch (1955), Yaglou & Minard (1957), Webb (1960) and Masterton & Richardson (1979). The following researches based on thermal physiological model are considered: Gagge (1967), Givoni (1969), Jendrizky (1979), Domínguez (1992), Brown & Gillespie (1995), Blazejczyk (1996), Höppe (1999), Pickup & Dear (1999) and Jendritzky (2003). The adaptative model of Aroztegui (1995) is presented and also two new empirical works: Givoni & Noguchi (2000) and Bluestein & Osczevski (2002). Last, the developing works of the Commission 6 of ISB (2004) are presented, which aim a universal thermal climate index. The contribution of this paper is a summarized historical review and current state-of-the-art in outdoor thermal comfort researches, presenting the equations and parameters proposed and a brief discussion of its limitations and possible new approaches. 1. Introduction Hipocrates (400bC) has already qualitatively described the main parameters that influence the thermal comfort: temperature, humidity, winds and radiation. The first registered temperatures measures were taken in Florence and Beijing, in the XVII century. During the XVIII century, thermal sensation opinions were collected, but they were always supposed to be evasive (Watson, 1979; apud Araujo, 1996). At the begging of the XIX century, in Europe, the first thermal stress studies were made, motivated by miners and textile workers health problems. Although some standardization has been already made, methods to measure variables and correlated them to thermal comfort were developed only in the begging of the XX century, motivated in part by the artificial air conditioning systems (Banham, 1975; apud Araujo, 1996). So, most researches focused just the relevant variables to typical indoor environment. Some of these studies were adapted to outdoors and others were specifically developed to it. This paper will present a review of the researches concerning outdoor thermal comfort, focusing the numerical modelling of their indexes. 2. First Indexes Houghten et al. (1923), of ASHVE laboratories, propose the Effective Temperature (ET), determined by dry and wet bulb temperature and wind speed. Researchs of Glickman, 1950; Smith, 1958 and Givoni, 1963 (apud Givoni, 1969) show that ET super estimate humidity. Vernon & Warner (1932) propose the New Effective Temperature (ET*) substituting dry bulb temperature by globe temperature. This index was adopted by ASHRAE, in 1967. McAriel et al. (1947) develop the Predictable Four Hour Sweat Rate - P4SR, based in physiological responses of four hour exposure to certain climate conditions. This index considers globe and wet bulb temperatures, wind speed, metabolism and two clothing ensembles. Missenard (1948), doing similar experiments to the Houghten, but with longer exposures, proposes the Resultante Temperature (RT). According to Givoni (1963, apud Givoni, 1969), this index presents better results than ET does. These four indexes were originally presented as nomogram charts and their equations were not originally published. 3. Wind Chill Temperature (WCT) Siple & Passel (1945; apud Williamson, 2003) developed the Wind Chill Temprature from the data obtained with experiences in Antarctica. The equipment were two plastics cylinders, filled with water, exposed to different temperatures (-9ºC~56ºC) and wind speeds (0m/s~12m/s). The water freezing time was observed. The experimental data was treated, generating a regression line. The equation proposed is: WCT = (12.15 + 11.6 • v10/2 - v10) • (33 - ta) (1) where: ta = air temperature, in ºC; v10 = air speed at 10m high, in m/s; -9ºC ≤ ta ≤ 10ºC; v10 ≤ 22.3m/s - 2252 - The 2005 World Sustainable Building Conference, Tokyo, 27-29 September 2005 (SB05Tokyo) 4. Heat Stress Index (HSI) Belding & Hatch (1955, apud Givoni, 1969) propose the Heat Stress Index. Considering the thermal balance model, they make four physiological suppositions: (1) the heat load in the body is equal to required evaporative sweat: Ersw = M + R + C; (2) the physiological strain is determined by the relation Ersw / Emax; (3) the skin temperature is constant during the thermal stress: tsk = 35°C; (4) the maximum sweat rate during an eight hour period is 1L/h, that is equivalent to 2400 Btu/h or 390 W/m2 for a male, 75 kg, 1.70m. The authors propose the following equations for estimating the heat storage: 0.5 Ersw = M + 22 · (trm - tsk) + 2 · v · (ta - tsk) (2) 0.4 Emax = 10 · v · (psk - pa) (3) where: [22 · (trm - tsk)] = radiation loads, in Btu/h; trm = mean radiant temperature, in ºF; tsk = superficial skin 0 5 temperature, in ºF; [2 · v , · (ta - tsk)] = convection loads, in Btu/h; ta = air temperature, in ºF; v = air speed, in ft/min; Ersw = required evaporative sweat, in Btu/h; Emax = maximum evaporative capacity, in Btu/h; psk = skin vapor pressure, in mmHg; pa = air vapor pressure, in mmHg Table 1 brings the index. It is determined, considering Ersw and Emax in W, by the greatest value between: HSI = (Ersw/Emax) ·100 & HSI = (Ersw/632.27) ·100 (4) This index is valid when: ta: 21-49 ºC; pa: 3-42 mmHg (22.5-315.0 kPa); v: 0.25-10.0 m/s and M: 86-430 W. Table 1: Heat Stress Index (HSI), Belding & Hatch (1955; apud Givoni, 1969 and Parsons, 1993) HSI Interpretation 0 - 10 no thermal stress (thermal comfort) 10 - 30 light response, intellectual work decrease as well as heavy mechanical work efficiency 40 - 60 several response, danger to non acclimatized people, mechanical work efficiency decrease 70 - 90 very several response, just little percentage of people support to work under such conditions 90 - 100 maximum response tolerated daily by acclimatized and adapted young man 100 - 200 heat storage (thermal stress) 5. Wet Bulb Globe Temperature (WBGT) Yaglou & Minard (1957) proposes the wet bulb globe temperature. Without direct solar radiation, the index is given by equation 5. With direct solar radiation, the index is given by equation 6 (ISO 7243, 1989). WBGT = 0.7 · tnwb + 0.3 · tg (5) WBGT = 0.7 · tnwb + 0.2 · tg + 0.1 ta (6) where: tg = globe temperature, in ºC; tnwb = natural wet bulb temperature, in ºC, ta = air temperature, in ºC 6. Equatorial Comfort Index (EC) Webb (1960, apud Santamouris & Asimakopoulos, 1996) developes the Equatorial Comfort Index, based on reseaches in Cingapure. The air temperature, pressure and speed data are correlated to the still and saturated air which would give the same thermal sensation. The experimental equation given is: 0,5 EC = 0.574 · ta + 0.2033 · pv - 1.8 · v + 42 (to twb > 25ºC and ta = trm) (7) where: ta = air temperature, in ºC; pa = vapor pressure, in mmHg; v = air speed, in m/s 7. New Standard Effective Temperature (SET*) Gagge (1967) presents the New Standard Effective Temperature (SET*), defining it as the air temperature in which, in a given reference environment, the person have the same skin temperature (tsk) and wettedness (w) that in the real environment. So, the reference and the real environments are equivalent in physiological strain and thermal comfort. The reference environment is defined as: mean radiant temperature (trm) = air temperature (ta); air speed (va) = 0.15 m/s; relative humidity (ur) = 50%; metabolism (M) = 1.2 met; clothes resistance (Iclo) = 0.9 clo. The SET* is determined by a two-node-model of human body thermal regulation, as proposed by Gagge et al. (1986), following the steps: (1) determination of tsk and w for a given environment; (2) input of tsk and w found, solving the equations to found a new air temperature (ta), considering trm=ta; v=0.15 m/s; ur=0.5; M=1.2 met; Iclo = 0.6 clo; (3) the ta found is the SET*. 8. The Index of Thermal Stress (ITS) Givoni (1969) proposes the Index of Thermal Stress, which considers the heat exchanges, metabolism and clothes. Originally, it did not consider the radiation exchanges. In order to consider them, the author suggests to use the globe temperature, instead of air temperature. Afterwards, solar radiation started to be The 2005 World Sustainable Building Conference, Tokyo, 27-29 September 2005 (SB05Tokyo) considered in the model. So, taking into account these adaptations and summarizing all the equations presented by the author in a unique equation, the index can be presented as: 0,3 0,2 ITS = {0.8 M + 20 + α · v · (tg - 35) + In · Kpe · Kcl · [1 - a · (v - 0.88)]} · (8) 0,3 0,3 · exp [ 0,6 · (0.8 M + 20 + α · v · (tg - 35) / p · v ·(42 - pv) - 0.12 )] where: M = metabolism, in kcal/h; α = clothing convective coefficient, dimensionless; v = air speed, in m/s; tg = globe temperature, in ºC; In = normal solar radiation, in kcal/h; Kpe = ground and posture coefficient, dimensionless; Kcl = clothing coefficient, dimensionless; a = clothing short wave radiation coefficient, dimensionless; p = clothing evaporative coefficient, dimensionless; pv = vapor pressure, in mmHg. According to the author (p. 91-92), α, Kcl, a, p are 15.8; 1.0; 0.35; 31.6 to bathing suit and hat and 13.0; 0.5; 0.52; 20.5 to lighting summer clothing.
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