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Combined simulation of airflow, radiation and moisture transport for heat release from a human body
Building and Environment 35 (2000) 489±500
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Combined simulation of air¯ow, radiation and moisture transport for heat release from a human body Shuzo Murakami a,*, Shinsuke Kato a, Jie Zeng b a
Institute of Industrial Science, University of Tokyo, Tokyo, Japan Institute for Research in Construction, National Research Council Canada, Ottawa, Canada
b
Received 29 March 1999; accepted 15 June 1999
Abstract This paper described a combined numerical simulation method of air¯ow, thermal radiation and moisture transport for predicting heat release from a human body. A human thermo-physiological model was also included to examine the sensible and latent heat transfer from the human body. Flow, temperature and moisture ®elds were investigated with three-dimensional Computational Fluid Dynamics (CFD). We used a low-Reynolds-number type k±E turbulence model, with the generalized curvilinear coordinate system to represent the complicated shape of the human body. The thermal radiation was calculated by means of Gebhart's absorption factor method, and the view factors were obtained by the Monte Carlo method. We adopted Gagge's two-node model to simulate the metabolic heat production and the thermoregulatory control processes of the human body. The predicted results were very close to those of an actual human body in a similar situation. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction CFD technique has been greatly developed in recent years. It is now possible for the HVAC researchers to numerically investigate complex indoor climates with sucient accuracy and acceptable CPU time [1±5]. Moreover, the coupled simulation of CFD and thermal radiation has also been developed and widely used [6± 8].1 This is of great advantage in analyzing thermal comfort of a human body since thermal radiation plays an important role in the thermal sensation of humans. * Corresponding author. Tel.: +81-33402-6231; fax: +81-337461449. E-mail address: [email protected] (S. Murakami). 1 In this paper, the word ``combined simulation'' meant the interactive analysis of the relationship between the indoor climate and the human body that included the thermo-physiological model, as shown by Part I and II in Fig. 2. Another word ``Coupled simulation'' was designated as the mathematical procedure for integrating CFD and radiant heat transfer, as shown by Part II in Fig. 2.
One of the most important research targets in the ®eld of HVAC is to investigate thermal sensation. Those studies used to be carried out by means of experiments [9±11]. However, recently researchers have also begun to numerically analyze thermal sensation on the basis of coupled simulation of CFD and radiation [3,8]. The human body not only has a complicated physical shape but also has complex thermo-physiological properties, thus it is very dicult to include those factors completely into the numerical simulation of an indoor climate. The previous studies used to simplify those two aspects. Concerning the complicated shape, most cases only regarded the human body as a heat source without physical shape. In a few studies, the human body was simpli®ed as a rectangle, a cylinder, or a ball [12]. Among those studies, the rectangle was the most frequently used to stand for the human body. We understood that the presence of the physical shape of the human body played a potential in¯uence on the indoor climate. Therefore the shape of the human body should be taken into consideration
0360-1323/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 1 3 2 3 ( 9 9 ) 0 0 0 3 3 - 5
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Nomenclature AD Bij cp,bl D Edif Emax Ersw Esk H hfg k K M mbl mrsw msk Pa Pa,ref Psk,s Qcd Qcv Qg Qm Qr Qres Qsk Qt Scr Ssk T Ta Tb
skin surface area of human body, m2 Gebhart's absorption factor speci®c heat of blood, 4.187 kJ/(kg K) hydraulic diameter, m diusion evaporative heat transfer rate from skin, W/m2 maximum evaporative potential from skin, W/m2 evaporative heat transfer by regulatory sweating from skin, W/m2 total evaporative heat transfer from skin, W/ m2 height of human body, m heat of vaporization of water, 2430 kJ/kg turbulent energy, m2/s2 eective conductance between the core node and the skin layer, 5.28 W/(m2 K) metabolic heat production, W/m2 blood ¯ow rate, kg/(m2s) regulatory sweat rate from skin, kg/(m2s) sweat rate generated from skin, kg/(m2s) water vapor pressure in ambient air, Pa water vapor pressure in ambient air outside the boundary layer of human body, Pa saturated water vapor pressure at Tsk at skin surface, Pa conductive heat transfer rate, W/m2 convective heat transfer rate, W/m2 heat generation rate, W/m2 total heat transfer rate of human body, W/m2 radiant heat transfer rate, W/m2 total heat transfer rate through respiration, W/m2 total (sensible+latent) heat transfer rate from skin, W/m2 sensible heat transfer rate, W/m2 rate of heat storage in core node, W/m2 rate of heat storage in skin layer, W/m2 mean temperature, K (radiation),8C (the other) ambient air temperature,8C mean body temperature,8C
in the balance of simulation load and simulation precision [3,13,14]. Another simpli®cation in the previous studies was to assume that the body surface had uniform temperature or uniform heat production without including the thermo-regulatory processes of the body in response to the environment [3,4,13±15]. To the author's knowledge, there are no previous numerical studies dealing with thermo-regulatory sweating [16]. Those studies apparently were
Tb,n mean body temperature at neutrality,8C Tcr temperature of core node of human body,8C Tcr,n neutral temperature of core node of human body, 36.88C Tsk temperature of skin layer,8C Tsk,n neutral temperature of skin layer, 33.78C wall surface temperature,8C Tw U mean velocity, m/s W weight of human body, kg w skin wettedness (including diusion and regulatory sweat) wrsw skin wettedness due to regulatory sweat X absolute humidity, g/kg y normal direction of wall, m y + distance from wall in viscous wall unit Greek letters evaporative heat transfer coecient, W/(m2 k ae Pa) b actual ratio of skin mass to whole mass of human body ratio of skin mass to whole body mass at neubn trality, 0.1, Ref. [11] 2 3 E dissipation prate 2 of turbulent energy, m /s , E=Eÿn(@ k/@y ) ; or surface emissivity for radiation l thermal conductivity, W/(m K) moisture conductive coecient in air, 3.082 lx 10ÿ5 kg/(m s) Subscripts a air cr core node i,j cell number in supply opening ref reference point outside boundary layer of human body sk skin layer s saturated state n thermal neutrality w wall surface l the ®rst cell near wall
not available to investigate the thermal sensation in a warm or hot environment, because thermo-regulatory sweating must appear in that kind of situation. Furthermore, the thermal sensation of humans is highly dependent on the local heat transfer characteristics of the body surface. The existence and metabolic heat production of the body can have a large in¯uence on the microclimate around the body. On the other hand, the local properties of the microclimate around
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Fig. 1. Flow®eld analyzed.
the body signi®cantly aect the local heat transfer characteristics of that body. Thus it is highly important to correctly analyze the interaction (heat and moisture transfer) between the human body and its surrounding microclimate [16]. This study developed a combined numerical simulation method of air¯ow, moisture transport (CFD), and thermal radiation integrating a human thermophysiological model to reproduce the complex heat production of the human body. This method was applied successfully to examine the total (sensible+latent) heat transfer characteristics of the human body. Therefore it has the potential capability of precisely predicting the thermal sensation of humans in various indoor environments.
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[17]. The room was air-conditioned in order to remove the heat and moisture production from the manikin. A displacement ventilation system was used to achieve the stagnant ¯ow ®eld in the room space (supply temperature: 228C, supply velocity: 0.12 m/s, air ¯ow rate: 57 m3/h, air change rate: 3.7 ACH). The walls around the room were adiabatic for both heat and moisture, assuming that the placement of the room would be in the interior part of a building. The shape of the manikin was slightly simpli®ed from that of a real human body with feet and arms put together, close to the body (Fig. 1), under the consideration of keeping the balance of simulation load and precision. The manikin had the standard height (1.651 m) and weight (65.5 kg) of a Japanese male adult, and thus the standard surface area (1.688 m2) [3]. 3. Combined numerical simulation method The combined numerical simulation method is illustrated in Fig. 2. The simulation was composed of two
2. Flow®eld analyzed The ¯ow®eld analyzed is shown in Fig. 1. As stated before, the aim of this study was to develop a combined numerical simulation system for investigating the total (sensible+latent) heat transfer characteristics of the human body. Our simulation target was a naked human body (manikin) standing in a stagnant environment.2 For the standing human body, the metabolic heat production M was suggested as 1.7 Met (100.4 W/m2) based on the ASHRAE handbook
2 In a previous paper [3,13,14] when analyzing the heat transfer from a human body, the internal heat transfer inside the skin surface was not dealt with. In that case, it was not necessry to de®ne whether the human body was naked or clothed. The boundary condition for that analysis was only the metabolic heat production. In this paper, it was necessary to specify the human body as being naked because the internal heat transfer was dealt with here. The skin surface temperature Tsk was calculated by the interactive analysis between the skin surface and the surrounding environment. However, the eect of clothing can be modeled without diculty by introducing the thermal and vapor resistance corresponding to the clothing following Gagge's model into the currently developed simulation system.
Fig. 2. Flow chart of combined simulation of air¯ow, radiation, and moisture transport.
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S. Murakami et al. / Building and Environment 35 (2000) 489±500 Table 1 Numerical methods Turbulence model
Low-Reynolds-number type k±E model (Launder±Sharma type)
Numerical schemes
Space dierence: hybrid
Grid system
Computational domain was discretized into 163,008 cells for CFD and 2232 cells for radiation with BFC. The y + of the ®rst cell near body and wall surface was less than 5. Only half space was calculated due to the symmetry of the ¯ow ®eld.
parts, which were combined at body surface through surface temperature as well as heat and mass balance equation. The aim and actual procedure of each part will be discussed in detail later. The ®rst part was to calculate the internal heat transfer inside the human body surface based on the human thermo-physiological model. For simplicity, we assumed that the heat loss through respiration was released directly into the environment without aecting the microclimate around the human body. According to this policy, the heat release rate through respiration Qres was ®xed as 8.7 W/m2 in advance from Eq. (A1) (Table A1), by assuming that the body was placed in a uniform environment (Ta=268C, Pa=1500 k Pa: the average situation around the human body). It should be noted that Qres was only speci®ed as the simulation input data due to its lesser in¯uence on the room environment. Other heat and mass transfer rates of the body were predicted from this simulation. The total (sensible+latent) heat release rate from skin Qsk was obtained as 91.7 W/m2 (=100.4±8.7), by excluding Qres from the metabolic heat production M. The second part of the simulation was to predict the heat and moisture transfer between the body surface and the surrounding environment by means of a coupled simulation of air¯ow, radiation and moisture transport.
3.1. Internal heat transfer: human thermo-physiological model Many human thermo-physiological models, including some elaborate multi-node models, were developed during the 1970s and 1980s [9±11,18,19]. Among those models, Fanger's model and Gagge's two-node model were widely applied for evaluating thermal sensation, because of their well-balanced performance and simplicity [17,20]. We also adopted those two models and examined their adaptability in our numerical simulation system. By comparing the results obtained from those two models, it became clear that Gagge's twonode model had wider adaptability, particularly in simulating sweating [21]. Therefore this paper only addresses the results obtained from Gagge's two-node model. Both Fanger's model and the two-node model, which dealt with whole-body heat balance rather than local balance, should be applied to the analysis of the whole body. However this study applied them locally, i.e., to each part of the body. The issues concerning the local application of those models will be discussed further. 3.2. Procedure of combined numerical simulation 3.2.1. Moisture transport Absolute humidity X was used to represent the
Table 2 Boundary conditions Supply opening
Uin=0.12 m/s, Tin=228C, Xin=9.5 g/kg, kin=0.002U 2in , Ein=k3=2 in /(0.3D ), D = 0.2 m
Exhaust opening
U, k, E, T, X: free slip
Wall boundary
U, k, E: Uw=0, kw=(@k/@y )w=0, Ew=0 Moisture: (@X/@y )w=0 (adiabatic wall) msk=ÿlx (@X/@y )w (body surface) Temperature: based on heat balance equation Qg=Qcd+Qr+Qcv (a) adiabatic wall: Qcd=0, Qg=0 body surface: Qcd=0, Qg=Qt (b) Qcv=ÿl(@T/@y )w=l(TwÿTl)/yl P 4 (c) Qr=sEiT 4i ÿ N jl BijsEiT j E: 0.98 (body), 0.95 (wall), 0.0 (opening and symmetrical surface)
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moisture transport. The transport equation used is shown in Eq. (1). @rX m r rUX r lx t rX 1 @t sx Here, moisture conductive coecient in air lx was 3.082 10ÿ5 kg/(m s) [22]. The turbulent Schmidt number sx was regarded as 1.0. 3.2.2. Numerical method We omitted the other transport equations for temperature, velocity, etc, because they were in the general form [23]. Flow, temperature and moisture ®elds were calculated with three-dimensional CFD. The CFD used the Launder±Sharma type low-Reynolds-number k±E turbulence model [23]. The thermal radiation was calculated by means of Gebhart's absorption factor method [24], and the view factors were obtained by the Monte Carlo method [25]. Table 1 shows the numerical methods for CFD and thermal radiation in detail. 3.2.3. Boundary conditions Appendix A describes the derivation of the boundary conditions for human body surface based on the two-node model. The sweat rate generated from the skin msk was calculated by using the two-node model in response to the room environment. This became the boundary condition of the body surface for solving the
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moisture transport equation (Eq. (1)). At the same time, the sensible heat loss from skin Qt was obtained by subtracting the latent heat release Esk from the total heat rate of skin Qsk. The Qt was used as the boundary condition of the human body surface for coupled simulation of heat convection and radiation. The method for coupled simulation of heat convection and radiation was described in detail in the previous study [8]. Table 2 shows the detailed boundary conditions for the human body and wall surfaces as well as for the supply and exhaust openings. 3.2.4. Flow chart of simulation Fig. 2 illustrates the ¯ow chart of the combined simulation of air¯ow, moisture transport and radiation based on the two-node model. For the internal heat transfer inside the body surface [Part I], sweat rate msk and sensible heat loss from skin Qt, was calculated by the given skin temperature Tsk and the environmental parameters Ta, U, X, Pa, Tw. The obtained values were used as boundary conditions for the combined simulation of air¯ow, radiation and moisture transport [Part II] (i.e., interactive heat transfer between the human body and its surrounding environment). As the outputs of Part II, the skin temperature Tsk and the environment parameters were renewed. The renewed values were fed back to the internal heat transfer part as calculation conditions. The iteration was continued until each variation became ®nally convergent.
Fig. 3. Predicted velocity ®eld (scalar and vector, Section ABCD, m/s,).
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¯ow patterns near the shoulder and above the head obtained from the visualization experiment. The predicted ¯ow patterns agreed very well with the experimental ones. The rising stream over the head reached a maximum velocity of 0.23 m/s from the numerical simulation. The predicted value also agreed with the measurement conducted by the authors, using the real human body (0.20 m/s) and the thermal manikin (0.21 m/s) [27]. The results were also consistent with a previous experiment [28]. 4.2. Distribution of air temperature Fig. 5 shows the distribution of air temperature around the manikin. A vertical temperature gradient was formed in the room due to the displacement ventilation system. The temperature dierence between the feet and head levels was approximately 3 or 48C. When convection and radiation were coupled, the vertical temperature gradient was not so steep compared to the results previously where only the convection was dealt with [3,13,14]. That dierence was caused by thermal radiation, which decreased the surface temperature dierence between the room walls. The ceiling, ¯oor and other walls were assumed to be adiabatic here. As a result, air temperature had a tendency to become uniform. In the upper region of the room above the manikin, the air temperature was higher and almost uniform at 278C.
Fig. 4. Flow visualization by experiment.
4. Results and discussion 4.1. Velocity distribution The velocity distribution of Section ABCD (Fig. 1) is shown in Fig. 3. A blanket of warm rising air was generated around the human body, whilst the ¯ow®eld apart from the manikin was almost stagnant. When the rising air passed from the neck to the head region, it was accelerated due to the contraction following the change of the body shape. In the upper region over the manikin, a rising thermal plume was clearly observed. The thickness of the velocity boundary layer around the manikin surface under the shoulders increased with respect to the height direction. This phenomenon was similar to the ¯ow pattern along a vertical heated ¯at plate [26]. The authors also carried out experiments of ¯ow visualization using both an experimental thermal manikin and a real human body [27]. Fig. 4 illustrated the
Fig. 5. Air temperature (Section ABCD, 8C).
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Fig. 6. Absolute humidity (g/kg).
4.3. Distribution of absolute humidity and relative humidity Figs. 6 and 7 show distribution of the absolute humidity and the relative humidity respectively. Moisture generated from the human body went up with the rising stream around the body surface. Consequently, the upper part of the space had the higher absolute humidity than the lower part. The distribution pattern of the absolute humidity was very similar to that of room air temperature. Concerning the relative humidity, it had higher values near the supply opening, where the temperature was low, because relative humidity also depends on temperature. The relative humidity was distributed pretty uniformly from 45 to 50% through the whole room space.
Fig. 7. Relative humidity.
from the human body by convection, radiation, evaporation and respiration respectively. One of the main purposes of this paper was to clarify the characteristics of the heat loss from a standing human body, which has the metabolic heat production of 1.7 Met, in a stagnant environment. That scenario corresponded to one of the most common situations in an actual building space. Therefore from this study the engineer can obtain some general concept on how much heat is nor-
4.4. Wall surface temperature Fig. 8 shows the distribution of wall surface temperature. The adiabatic walls of the room gained heat from the human body by radiation, and then released the same quantity of heat to the air by convection. Thus the wall surface temperatures were generally approximately 0.38C higher than the room air temperature. The radiant heat transfer also occurred between the walls, due to the temperature dierence between the wall surfaces. That caused the trend of wall surface temperature to become uniform [3,13,14]. 4.5. Heat release characteristics from human body Fig. 9 illustrates the mean heat release quantity
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Fig. 8. Wall surface temperature (8C).
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Fig. 9. Heat release from human body (W/m2).
mally released from the human body through each route. As shown in Fig. 9, the human body released its metabolic heat production (1.7 Met) to the surround environment, 49.3 W (29.1 W/m2) by convection, 65.1 W (38.3 W/m2) by radiation, 41.3 W (24.3 W/m2) by evaporation and 14.8 W (8.7 W/m2) by respiration. As a total percentage of the entire heat released from the human body approximately 29.0% was by convection, 38.1% by radiation, 24.2% by evaporation and 8.7% by respiration under the conditions of this simulation. The human body released the most heat by radiation. This suggested that radiation played a signi®cant in¯uence on thermal sensation of the human body. 4.6. Heat balance between manikin and room walls Fig. 10 shows the heat balance between the manikin and the room walls. The ¯oor temperature was the lowest, generally 1.08C lower than that of the other walls (Fig. 8). Thus, the ¯oor gained the largest radiant heat 33.8 W in total from the human body as well as from the other walls. Conversely, the ceiling had the highest temperature. Therefore the ceiling released heat by radiation (5.5 W) to the other walls and gained heat from the air by convection. The side walls of the
Fig. 11. Surface temperature of human body.
room got less heat by radiation compared to the front and rear wall due to the smaller view factor between the human body (main radiation heat source) and the side walls. This can be easily understood from the location relationship since the human body faced the front wall. Concerning the two side walls, the radiant heat transfer rates were not equal to each other, although their surface temperatures were almost symmetrical (Fig. 8). That slight dierence was caused by the unsymmetrical distribution of the surface temperature of the human body. The right side of the human body facing the supply opening had lower skin temperature than the left side (Fig. 11). Thus the side wall with the supply opening gained slightly lower radiant heat from the human body than the opposite side wall with the exhaust opening.
4.7. Temperature of manikin skin surface
Fig. 10. Heat balance between human body and its environment.
Fig. 11 shows temperature distribution of the manikin skin surface. It generally ranged from 33.0 to 34.08C. It decreased below 29.08C at the right foot facing the supply opening, and increased above 34.08C at the neck and the shoulders. The previous experimental results [29] demonstrated a similar tendency of temperature distribution on the skin surface of a real human body. The mean skin surface temperature was calculated at 33.38C. This value was slightly lower than that of a human body in the state of physiological thermal neutrality (33.78C) with normal indoor activity [17].
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Fig. 12. Convective heat transfer characteristics of human body surface.
4.8. Convective heat transfer characteristics of manikin surface Fig. 12 illustrates the convective heat transfer rate and heat transfer coecient of the manikin skin surface. Both distribution patterns were similar to one another. The values were larger at the feet because of the thinner boundary layer at that location. They decreased with respect to the height direction of manikin. That kind of distribution corresponded to those of the vertical heated ¯at plate (heat and mass transfer book). The convective heat transfer rate ranged from 20.0 to 40.0 W/m2. The convective heat transfer coecient ranged from 3.0 to 4.0 W/(m2 K). It increased to 7.0 W/(m2 K) at the feet. The mean convective heat transfer coecient was determined to be 4.3 W/(m2 K). The results of mean value and distribution characteristics of the convective heat transfer coecient were in agreement with previous experiments [17,30,31]. 4.9. Radiant heat transfer characteristics of manikin surface Fig. 13(1) shows radiant heat transfer rate of the manikin surface. Neither the temperature dierence 3 More accurately, this concept is speci®ed as the plane radiative temperature, which is the average at each small plane on the body surface.
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Fig. 13. Radiant heat transfer characteristics of human body surface.
among the room walls nor that at the manikin surface were signi®cantly large, thus the radiant heat transfer of the manikin surface ranged uniformly from 30.0 to 40.0 W/m2. The feet, however, had slightly smaller values due to the lower manikin surface temperature there. On average, the heat transfer by radiation (38.3 W/m2) was larger than that by convection (29.1 W/ m2). Fig. 13(2) shows the distribution of mean radiant temperature of the manikin surface. It was distributed almost uniformly from 27.0 to 28.08C.3 The left and right sides of the manikin had the low mean radiant temperature due to the large view factors of those parts towards the ¯oor, where temperature was low. 4.10. Evaporative heat transfer characteristics of manikin surface Fig. 14(1) shows the evaporative heat transfer rate of the body surface. It ranged from 20.0 to 30.0 W/m2. In this study it was assumed that the total (sensible+latent) heat loss rate was the same over the whole manikin surface. Consequently, the evaporative heat transfer rate decreased below 20.0 W/m2 at the feet, due to the large sensible heat transfer rate at that point. The evaporative heat transfer rate increased over 30.0 W/m2 at the shoulders. These results corresponded to previous experimental results [22]. Fig. 14(2) shows the evaporative heat transfer coecient of the manikin surface. The distribution characteristics were similar to that of the convective heat transfer coecient. Due to the thin boundary layer at
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Fig. 16. Blood ¯ow rate of human body. Fig. 14. Evaporative heat transfer characteristics of human body surface.
the feet, a large coecient value appeared there and decreased with respect to the height direction of the body. The evaporative heat transfer coecient generally ranged from 60.0 to 80.0 W/(m2 k Pa) over the manikin surface. The mean value was calculated as 70.2 W/(m2 k Pa). Using the ratio to mean convective heat transfer coecient 4.3 W/(m2 K), the Lewis ratio was obtained as 16.58C/k Pa, the exact same as the value recommended by ASHRAE [17].
4.11. Skin wettedness Fig. 15 shows the skin wettedness of the manikin surface. The evaporative heat transfer rate at the feet was low, causing the skin wettedness to also be low there at 0.06. That value (0.06) suggested that only diffusive evaporation occurred and that regulatory sweating was not generated at the feet in this environmental condition. The skin wettedness increased with respect to the height direction of the body. It reached the maximum value of over 0.18 at the shoulders. That distribution property corresponded to the actual situation of a real human body [22]. The mean value was 0.11. It also corresponded to that of a human body in thermal neutrality with the activity level of 1.7 Met. 4.12. Other physiological parameters of manikin The core temperature of the manikin was almost 36.98C everywhere (data not shown). It was almost the same as the neutral core temperature of 36.88C. Fig. 16 shows the skin blood ¯ow rate of the manikin. It generally ranged from 4.0 to 6.0 g/(s m2) over the manikin surface. The blood ¯ow rate was below 2.0 g/(s m2) at the feet. It increased above 7.0 g/(s m2) at the shoulders and the neck. This distribution property corresponded to the manikin surface temperature (Fig. 11).
5. Concluding remarks Fig. 15. Skin wettedness of human body.
A combined numerical simulation system was devel-
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Table A1 Derivation of boundary conditions of human body surface [11] Heat loss from respiration Qres Qres=0.014 M(34.0ÿTa)+1.73 10ÿ5M(5.87 103ÿPa)
(A1)
Heat balance equations for body core and skin layer Scr=(QmÿQres)ÿK(TcrÿTsk)ÿcp,blmbl(TcrÿTsk) Ssk=K(TcrÿTsk)+cp,blmbl(TcrÿTsk)ÿEskÿ(Qcv+Qr)
(A2) (A3)
Thermal neutrality for body core, skin layer, and whole body Tcr,n=36.88C Tsk,n=33.78C Tb,n=bnTsk,n+(1ÿbn)Tcr,n
(A4) (A5) (A6)
Thermo-regulatory control processes (vasomotor regulation and sweating) mbl=[(6.3+200WSIGcr)/(1+0.1CSIGsk)]/3600 mrsw=4.72 10ÿ5WSIGbexp(WSIGsk/10.7) b=0.042+0.745/(3600 mbl+0.585)
(A7) (A8) (A9)
Temperature signals WSIGcr=max((TcrÿTcr,n),0) CSIGsk=max((Tsk,nÿTsk),0) WSIGb=max((TbÿTb,n),0) WSIGsk=max((TskÿTsk,n),0) Tb=bTsk+(1ÿb )Tcr
(A10) (A11) (A12) (A13) (A14)
Boundary conditions for solving moisture transport equation Ersw=mrswhfg wrsw=Ersw/Emax Edif=(1ÿwrsw)0.06Emax w=wrsw+0.06(1ÿwrsw)=0.06+0.94Ersw/Emax Esk=wEmax Emax=ae(Psk,sÿPa,ref) msk=Esk/hfg
(A15) (A16) (A17) (A18) (A19) (A20) (A21)
Boundary conditions for coupled simulation of heat convection and radiation Qt=QmÿQresÿEsk
(A22)
oped for predicting air¯ow, moisture transport, and thermal radiation based on a human thermo-physiological model. That system made it possible to investigate precisely the distributions of both sensible and latent heat transfer characteristics at the skin surface of the human body. The two-node model was used here. It was originally developed for applying to the whole body heat budget. In its original concept it could not be applied to analyze the local heat transfer as was carried out in this study. However, when adapting it locally to body surface, the obtained heat transfer characteristics of the body corresponded with the actual phenomena of the real human body. The use of the two-node model locally at the body surface seemed tolerable in such analyses. The multi-node model will be further examined at the next stage. Thermal sensation indices such as SET and PMV can be reported based on the results of this study. Human's thermal sensation thus can be further predicted precisely by means of the combined numerical prediction system developed in this study.
Appendix A Boundary conditions of body surface were derived based on the two-node model. Table A1 shows the setup of the equations. The two-node model [10,11] represented the body as two concentric cylinders, i.e., the inner cylinder referred to the body core and the outer cylinder referred to the skin layer. The metabolic heat production at the core was released to the environment by two routes. The major one was to transfer heat to the skin by blood ¯ow and heat conduction, and to be released from the skin to the environment by convection, radiation and evaporation. The minor one was a direct release to the environment through respiration (Eq. A1). As shown in Eqs. (A2) and (A3), two heat balance equations for the body core and the skin layer were built up. Here the steady state was assumed; thus the rates of heat storage, Scr and Ssk, were regarded as zero. When the body was in the state of thermal neutrality physiologically, the mean temperatures of the core node Tcr,n, the skin layer Tsk,n, and the entire body
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Tb,n were at their neutral values (Eqs. (A4)±(A6)). If the temperature deviated from neutrality, the thermoregulatory control processes (vasomotor regulation, sweating, and shivering) occurred. These processes were simulated through the temperature signals as shown in Eqs. (A7) and (A8). The temperature signals were speci®ed in Eqs. from (A10) to (A13). The mean body temperature Tb was calculated from Eq. (A14). The actual ratio of the skin mass to the whole body mass b was calculated from Eq. (A9), because of its dependency on the blood ¯ow rate. The evaporative heat loss by regulatory sweating Ersw and the skin wettedness due to regulatory sweating wrsw were calculated from Eqs. (A15) and (A16), respectively, by the speci®ed regulatory sweat rate mrsw. With no regulatory sweating, the skin wettedness due to diusion was 0.06 for normal conditions. Then the diusion evaporative heat loss Edif was calculated from Eq. (A17). The total evaporative heat loss from skin Esk was shown in Eq. (A19). The total sweat rate generated from skin msk was simply calculated from Eq. (A21). That value became the boundary condition of the body surface for solving the moisture transport equation. The sensible heat loss from skin Qt was derived as Eq. (A22). It became the boundary condition of the human body surface for coupled simulation of heat convection and radiation. References [1] Murakami S. Prediction, analysis and design for indoor climate in large enclosures. ROOMVENT'92 1992;1:1±30. [2] Kato S, Murakami S, Shoya S, Hanyu F, Zeng J. CFD analysis of ¯ow and temperature ®elds in atrium with ceiling height of 130 m. ASHRAE Transactions 1994;95(2). [3] Murakami S, Kato S, Zeng J. Flow and temperature ®elds around human body with various room air distribution, CFD study on computational thermal manikin (Part 1). ASHRAE Transactions 1997;103(1):3±15. [4] Murakami S, Kato S, Zeng J. Numerical simulation of contaminant distribution around a modeled human body, CFD study on computational thermal manikin (Part 2). ASHRAE Transactions 1998;104(2). [5] Chen Q. Computational ¯uid dynamics for HVAC: successes and failures. ASHRAE Transactions 1997;103(1):178±87. [6] Murakami S, Kato S, Kondo Y, Takahashi Y, Choi D. Numerical study on thermal environment in air-conditioned room by means of coupled simulation of convective and radiative heat transport, method for coupling convective simulation and radiative simulation (Part 1). Transactions of the Society of Heating, Air-Conditioning and Sanitary Engineers of Japan (SHASE) 1995;57:105±16 [in Japanese]. [7] Murakami S, Kato S, Choi D, Kobayashi H, Omori T. Numerical study on thermal environment in air-conditioned room by means of coupled simulation of convective and radiative heat transport, accuracy of shape factor calculation by modi®ed Monte Carlo method and its application for a room with complex geometry (Part 2). SHASE Transactions 1995;59:95±104 [in Japanese]. [8] Murakami S, Kato S, Zeng J. Coupled simulation of convective and radiant heat transfer around standing human body, study
[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
[22] [23] [24] [25] [26]
[27]
[28] [29] [30] [31]
on computational thermal manikin (Part 3). Transactions of J Archit Plann Environ Eng, AIJ 1999;515:69±74 [in Japanese]. Fanger PO. Thermal comfort. Danish Technical Press, 1970. Gagge AP, Stolwijk JAJ, Nishi Y. An eective temperature scale based on a simple model of human physiological regulatory response. ASHRAE Transactions 1970;77(1):247±62. Gagge AP, Fobelets AP, Berglund LG. A standard predictive index of human response to the thermal environment. ASHRAE Transactions 1986;92(1):709±31. Brohus H, Nielsen PV. Personal exposure to contaminant sources in a uniform velocity ®eld. Healthy Buildings '95, 1995. Murakami S, Kato S, Zeng J. Development of a computational thermal manikin, CFD analysis of thermal environment around human body. Tsinghua-HVAC '95 1995;2:349±54. Murakami S, Kato S, Zeng J. CFD analysis of thermal environment around human body. Indoor air '96 1996;2:479±84. Kato S, Murakami S, Zeng J. Numerical analysis of contaminant distribution around a human body. ROOMVENT '96 1996;2:129±36. Kato S, Murakami S, Zeng J. Combined simulation of air¯ow, radiation and moisture transport for heat release from human body. ROOMVENT '98 1998;2:141±50. ASHRAE fundamentals handbook, [Chapter 8] 1993. Gordon RG, Rober RB, Horvath SM. IEEE Trans 1976;BME23:434±44. Stolwijk JAJ. A mathematical model of physiological temperature regulation in man. NASA contractor report, NASA CR1855, 1971. Yokoyama S, Ochihuji S, Nagano K. Journal of the Heat Transfer Society of Japan 1994;33(131):41±50 [in Japanese]. Zeng J, Kato S, Murakami S. Coupled simulation of CFD, radiation and moisture transport for sensible and latent heat loss from human body, study of computational thermal manikin. SEISAN-KENKYU, Monthly Journal of Institute of Industrial Science, University of Tokyo 1998;50(1):78±85 [in Japanese]. Nakayama S. Thermophysiology. Tokyo: Rikougakusya Press, 1987 [in Japanese]. Launder BE, Sharma BI. Application of the energy-dissipation model of turbulence to the calculation of ¯ow near a spinning disc. Letters in Heat and Mass Transfer 1974;1:131±8. Gebhart B. A new method for calculating radiant exchanges. ASHRAE Trans 1959;65:321±3. Omori T, Taniguchi H, Kudo K. Prediction method of radiant environment in a room and its application to ¯oor heating. SHASE Trans 1990;42:9±18 [in Japanese]. Kato S, Murakami S, Yoshie R. Experimental and numerical study on natural convection with strong density variation along a heated vertical plate. In: Proceedings of the Ninth Symposium on Turbulent Shear Flows, 1993. p. 5±12. Hayashi T, Murakami S, Kato S, Takahashi T, Zeng J, Sakuma K. Study on computational thermal manikin (Part 14), Measurement of ¯ow and temperature ®elds around real human body and thermal manikin. In: Proceedings of the Annual Technical Conference of SHASE, 1998. 2. p. 985±988. [in Japanese]. Homma H, Yakiyama M. Examination of free convection around occupant's body caused by it's metabolic heat. ASHRAE Trans 1988;94(1):104±24. Torikai K, Suzuki K, Tsutaki S. Thermal emission from human body. In: Proceedings of the Second JSME-KSME Thermal Engineering Conference, 1992. Nielsen M, Pedersen L. Studies on the heat loss by radiation and convection from the clothed human body. Acta Phys Scandinav 1952;27:272±94. Rapp GM. Convective heat transfer and convective coecients of nude man, cylinders and spheres at low velocities. ASHRAE Trans 1973;2264:75±87.
www.elsevier.com/locate/buildenv
Combined simulation of air¯ow, radiation and moisture transport for heat release from a human body Shuzo Murakami a,*, Shinsuke Kato a, Jie Zeng b a
Institute of Industrial Science, University of Tokyo, Tokyo, Japan Institute for Research in Construction, National Research Council Canada, Ottawa, Canada
b
Received 29 March 1999; accepted 15 June 1999
Abstract This paper described a combined numerical simulation method of air¯ow, thermal radiation and moisture transport for predicting heat release from a human body. A human thermo-physiological model was also included to examine the sensible and latent heat transfer from the human body. Flow, temperature and moisture ®elds were investigated with three-dimensional Computational Fluid Dynamics (CFD). We used a low-Reynolds-number type k±E turbulence model, with the generalized curvilinear coordinate system to represent the complicated shape of the human body. The thermal radiation was calculated by means of Gebhart's absorption factor method, and the view factors were obtained by the Monte Carlo method. We adopted Gagge's two-node model to simulate the metabolic heat production and the thermoregulatory control processes of the human body. The predicted results were very close to those of an actual human body in a similar situation. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction CFD technique has been greatly developed in recent years. It is now possible for the HVAC researchers to numerically investigate complex indoor climates with sucient accuracy and acceptable CPU time [1±5]. Moreover, the coupled simulation of CFD and thermal radiation has also been developed and widely used [6± 8].1 This is of great advantage in analyzing thermal comfort of a human body since thermal radiation plays an important role in the thermal sensation of humans. * Corresponding author. Tel.: +81-33402-6231; fax: +81-337461449. E-mail address: [email protected] (S. Murakami). 1 In this paper, the word ``combined simulation'' meant the interactive analysis of the relationship between the indoor climate and the human body that included the thermo-physiological model, as shown by Part I and II in Fig. 2. Another word ``Coupled simulation'' was designated as the mathematical procedure for integrating CFD and radiant heat transfer, as shown by Part II in Fig. 2.
One of the most important research targets in the ®eld of HVAC is to investigate thermal sensation. Those studies used to be carried out by means of experiments [9±11]. However, recently researchers have also begun to numerically analyze thermal sensation on the basis of coupled simulation of CFD and radiation [3,8]. The human body not only has a complicated physical shape but also has complex thermo-physiological properties, thus it is very dicult to include those factors completely into the numerical simulation of an indoor climate. The previous studies used to simplify those two aspects. Concerning the complicated shape, most cases only regarded the human body as a heat source without physical shape. In a few studies, the human body was simpli®ed as a rectangle, a cylinder, or a ball [12]. Among those studies, the rectangle was the most frequently used to stand for the human body. We understood that the presence of the physical shape of the human body played a potential in¯uence on the indoor climate. Therefore the shape of the human body should be taken into consideration
0360-1323/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 1 3 2 3 ( 9 9 ) 0 0 0 3 3 - 5
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Nomenclature AD Bij cp,bl D Edif Emax Ersw Esk H hfg k K M mbl mrsw msk Pa Pa,ref Psk,s Qcd Qcv Qg Qm Qr Qres Qsk Qt Scr Ssk T Ta Tb
skin surface area of human body, m2 Gebhart's absorption factor speci®c heat of blood, 4.187 kJ/(kg K) hydraulic diameter, m diusion evaporative heat transfer rate from skin, W/m2 maximum evaporative potential from skin, W/m2 evaporative heat transfer by regulatory sweating from skin, W/m2 total evaporative heat transfer from skin, W/ m2 height of human body, m heat of vaporization of water, 2430 kJ/kg turbulent energy, m2/s2 eective conductance between the core node and the skin layer, 5.28 W/(m2 K) metabolic heat production, W/m2 blood ¯ow rate, kg/(m2s) regulatory sweat rate from skin, kg/(m2s) sweat rate generated from skin, kg/(m2s) water vapor pressure in ambient air, Pa water vapor pressure in ambient air outside the boundary layer of human body, Pa saturated water vapor pressure at Tsk at skin surface, Pa conductive heat transfer rate, W/m2 convective heat transfer rate, W/m2 heat generation rate, W/m2 total heat transfer rate of human body, W/m2 radiant heat transfer rate, W/m2 total heat transfer rate through respiration, W/m2 total (sensible+latent) heat transfer rate from skin, W/m2 sensible heat transfer rate, W/m2 rate of heat storage in core node, W/m2 rate of heat storage in skin layer, W/m2 mean temperature, K (radiation),8C (the other) ambient air temperature,8C mean body temperature,8C
in the balance of simulation load and simulation precision [3,13,14]. Another simpli®cation in the previous studies was to assume that the body surface had uniform temperature or uniform heat production without including the thermo-regulatory processes of the body in response to the environment [3,4,13±15]. To the author's knowledge, there are no previous numerical studies dealing with thermo-regulatory sweating [16]. Those studies apparently were
Tb,n mean body temperature at neutrality,8C Tcr temperature of core node of human body,8C Tcr,n neutral temperature of core node of human body, 36.88C Tsk temperature of skin layer,8C Tsk,n neutral temperature of skin layer, 33.78C wall surface temperature,8C Tw U mean velocity, m/s W weight of human body, kg w skin wettedness (including diusion and regulatory sweat) wrsw skin wettedness due to regulatory sweat X absolute humidity, g/kg y normal direction of wall, m y + distance from wall in viscous wall unit Greek letters evaporative heat transfer coecient, W/(m2 k ae Pa) b actual ratio of skin mass to whole mass of human body ratio of skin mass to whole body mass at neubn trality, 0.1, Ref. [11] 2 3 E dissipation prate 2 of turbulent energy, m /s , E=Eÿn(@ k/@y ) ; or surface emissivity for radiation l thermal conductivity, W/(m K) moisture conductive coecient in air, 3.082 lx 10ÿ5 kg/(m s) Subscripts a air cr core node i,j cell number in supply opening ref reference point outside boundary layer of human body sk skin layer s saturated state n thermal neutrality w wall surface l the ®rst cell near wall
not available to investigate the thermal sensation in a warm or hot environment, because thermo-regulatory sweating must appear in that kind of situation. Furthermore, the thermal sensation of humans is highly dependent on the local heat transfer characteristics of the body surface. The existence and metabolic heat production of the body can have a large in¯uence on the microclimate around the body. On the other hand, the local properties of the microclimate around
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Fig. 1. Flow®eld analyzed.
the body signi®cantly aect the local heat transfer characteristics of that body. Thus it is highly important to correctly analyze the interaction (heat and moisture transfer) between the human body and its surrounding microclimate [16]. This study developed a combined numerical simulation method of air¯ow, moisture transport (CFD), and thermal radiation integrating a human thermophysiological model to reproduce the complex heat production of the human body. This method was applied successfully to examine the total (sensible+latent) heat transfer characteristics of the human body. Therefore it has the potential capability of precisely predicting the thermal sensation of humans in various indoor environments.
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[17]. The room was air-conditioned in order to remove the heat and moisture production from the manikin. A displacement ventilation system was used to achieve the stagnant ¯ow ®eld in the room space (supply temperature: 228C, supply velocity: 0.12 m/s, air ¯ow rate: 57 m3/h, air change rate: 3.7 ACH). The walls around the room were adiabatic for both heat and moisture, assuming that the placement of the room would be in the interior part of a building. The shape of the manikin was slightly simpli®ed from that of a real human body with feet and arms put together, close to the body (Fig. 1), under the consideration of keeping the balance of simulation load and precision. The manikin had the standard height (1.651 m) and weight (65.5 kg) of a Japanese male adult, and thus the standard surface area (1.688 m2) [3]. 3. Combined numerical simulation method The combined numerical simulation method is illustrated in Fig. 2. The simulation was composed of two
2. Flow®eld analyzed The ¯ow®eld analyzed is shown in Fig. 1. As stated before, the aim of this study was to develop a combined numerical simulation system for investigating the total (sensible+latent) heat transfer characteristics of the human body. Our simulation target was a naked human body (manikin) standing in a stagnant environment.2 For the standing human body, the metabolic heat production M was suggested as 1.7 Met (100.4 W/m2) based on the ASHRAE handbook
2 In a previous paper [3,13,14] when analyzing the heat transfer from a human body, the internal heat transfer inside the skin surface was not dealt with. In that case, it was not necessry to de®ne whether the human body was naked or clothed. The boundary condition for that analysis was only the metabolic heat production. In this paper, it was necessary to specify the human body as being naked because the internal heat transfer was dealt with here. The skin surface temperature Tsk was calculated by the interactive analysis between the skin surface and the surrounding environment. However, the eect of clothing can be modeled without diculty by introducing the thermal and vapor resistance corresponding to the clothing following Gagge's model into the currently developed simulation system.
Fig. 2. Flow chart of combined simulation of air¯ow, radiation, and moisture transport.
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S. Murakami et al. / Building and Environment 35 (2000) 489±500 Table 1 Numerical methods Turbulence model
Low-Reynolds-number type k±E model (Launder±Sharma type)
Numerical schemes
Space dierence: hybrid
Grid system
Computational domain was discretized into 163,008 cells for CFD and 2232 cells for radiation with BFC. The y + of the ®rst cell near body and wall surface was less than 5. Only half space was calculated due to the symmetry of the ¯ow ®eld.
parts, which were combined at body surface through surface temperature as well as heat and mass balance equation. The aim and actual procedure of each part will be discussed in detail later. The ®rst part was to calculate the internal heat transfer inside the human body surface based on the human thermo-physiological model. For simplicity, we assumed that the heat loss through respiration was released directly into the environment without aecting the microclimate around the human body. According to this policy, the heat release rate through respiration Qres was ®xed as 8.7 W/m2 in advance from Eq. (A1) (Table A1), by assuming that the body was placed in a uniform environment (Ta=268C, Pa=1500 k Pa: the average situation around the human body). It should be noted that Qres was only speci®ed as the simulation input data due to its lesser in¯uence on the room environment. Other heat and mass transfer rates of the body were predicted from this simulation. The total (sensible+latent) heat release rate from skin Qsk was obtained as 91.7 W/m2 (=100.4±8.7), by excluding Qres from the metabolic heat production M. The second part of the simulation was to predict the heat and moisture transfer between the body surface and the surrounding environment by means of a coupled simulation of air¯ow, radiation and moisture transport.
3.1. Internal heat transfer: human thermo-physiological model Many human thermo-physiological models, including some elaborate multi-node models, were developed during the 1970s and 1980s [9±11,18,19]. Among those models, Fanger's model and Gagge's two-node model were widely applied for evaluating thermal sensation, because of their well-balanced performance and simplicity [17,20]. We also adopted those two models and examined their adaptability in our numerical simulation system. By comparing the results obtained from those two models, it became clear that Gagge's twonode model had wider adaptability, particularly in simulating sweating [21]. Therefore this paper only addresses the results obtained from Gagge's two-node model. Both Fanger's model and the two-node model, which dealt with whole-body heat balance rather than local balance, should be applied to the analysis of the whole body. However this study applied them locally, i.e., to each part of the body. The issues concerning the local application of those models will be discussed further. 3.2. Procedure of combined numerical simulation 3.2.1. Moisture transport Absolute humidity X was used to represent the
Table 2 Boundary conditions Supply opening
Uin=0.12 m/s, Tin=228C, Xin=9.5 g/kg, kin=0.002U 2in , Ein=k3=2 in /(0.3D ), D = 0.2 m
Exhaust opening
U, k, E, T, X: free slip
Wall boundary
U, k, E: Uw=0, kw=(@k/@y )w=0, Ew=0 Moisture: (@X/@y )w=0 (adiabatic wall) msk=ÿlx (@X/@y )w (body surface) Temperature: based on heat balance equation Qg=Qcd+Qr+Qcv (a) adiabatic wall: Qcd=0, Qg=0 body surface: Qcd=0, Qg=Qt (b) Qcv=ÿl(@T/@y )w=l(TwÿTl)/yl P 4 (c) Qr=sEiT 4i ÿ N jl BijsEiT j E: 0.98 (body), 0.95 (wall), 0.0 (opening and symmetrical surface)
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moisture transport. The transport equation used is shown in Eq. (1). @rX m r rUX r lx t rX 1 @t sx Here, moisture conductive coecient in air lx was 3.082 10ÿ5 kg/(m s) [22]. The turbulent Schmidt number sx was regarded as 1.0. 3.2.2. Numerical method We omitted the other transport equations for temperature, velocity, etc, because they were in the general form [23]. Flow, temperature and moisture ®elds were calculated with three-dimensional CFD. The CFD used the Launder±Sharma type low-Reynolds-number k±E turbulence model [23]. The thermal radiation was calculated by means of Gebhart's absorption factor method [24], and the view factors were obtained by the Monte Carlo method [25]. Table 1 shows the numerical methods for CFD and thermal radiation in detail. 3.2.3. Boundary conditions Appendix A describes the derivation of the boundary conditions for human body surface based on the two-node model. The sweat rate generated from the skin msk was calculated by using the two-node model in response to the room environment. This became the boundary condition of the body surface for solving the
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moisture transport equation (Eq. (1)). At the same time, the sensible heat loss from skin Qt was obtained by subtracting the latent heat release Esk from the total heat rate of skin Qsk. The Qt was used as the boundary condition of the human body surface for coupled simulation of heat convection and radiation. The method for coupled simulation of heat convection and radiation was described in detail in the previous study [8]. Table 2 shows the detailed boundary conditions for the human body and wall surfaces as well as for the supply and exhaust openings. 3.2.4. Flow chart of simulation Fig. 2 illustrates the ¯ow chart of the combined simulation of air¯ow, moisture transport and radiation based on the two-node model. For the internal heat transfer inside the body surface [Part I], sweat rate msk and sensible heat loss from skin Qt, was calculated by the given skin temperature Tsk and the environmental parameters Ta, U, X, Pa, Tw. The obtained values were used as boundary conditions for the combined simulation of air¯ow, radiation and moisture transport [Part II] (i.e., interactive heat transfer between the human body and its surrounding environment). As the outputs of Part II, the skin temperature Tsk and the environment parameters were renewed. The renewed values were fed back to the internal heat transfer part as calculation conditions. The iteration was continued until each variation became ®nally convergent.
Fig. 3. Predicted velocity ®eld (scalar and vector, Section ABCD, m/s,).
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¯ow patterns near the shoulder and above the head obtained from the visualization experiment. The predicted ¯ow patterns agreed very well with the experimental ones. The rising stream over the head reached a maximum velocity of 0.23 m/s from the numerical simulation. The predicted value also agreed with the measurement conducted by the authors, using the real human body (0.20 m/s) and the thermal manikin (0.21 m/s) [27]. The results were also consistent with a previous experiment [28]. 4.2. Distribution of air temperature Fig. 5 shows the distribution of air temperature around the manikin. A vertical temperature gradient was formed in the room due to the displacement ventilation system. The temperature dierence between the feet and head levels was approximately 3 or 48C. When convection and radiation were coupled, the vertical temperature gradient was not so steep compared to the results previously where only the convection was dealt with [3,13,14]. That dierence was caused by thermal radiation, which decreased the surface temperature dierence between the room walls. The ceiling, ¯oor and other walls were assumed to be adiabatic here. As a result, air temperature had a tendency to become uniform. In the upper region of the room above the manikin, the air temperature was higher and almost uniform at 278C.
Fig. 4. Flow visualization by experiment.
4. Results and discussion 4.1. Velocity distribution The velocity distribution of Section ABCD (Fig. 1) is shown in Fig. 3. A blanket of warm rising air was generated around the human body, whilst the ¯ow®eld apart from the manikin was almost stagnant. When the rising air passed from the neck to the head region, it was accelerated due to the contraction following the change of the body shape. In the upper region over the manikin, a rising thermal plume was clearly observed. The thickness of the velocity boundary layer around the manikin surface under the shoulders increased with respect to the height direction. This phenomenon was similar to the ¯ow pattern along a vertical heated ¯at plate [26]. The authors also carried out experiments of ¯ow visualization using both an experimental thermal manikin and a real human body [27]. Fig. 4 illustrated the
Fig. 5. Air temperature (Section ABCD, 8C).
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Fig. 6. Absolute humidity (g/kg).
4.3. Distribution of absolute humidity and relative humidity Figs. 6 and 7 show distribution of the absolute humidity and the relative humidity respectively. Moisture generated from the human body went up with the rising stream around the body surface. Consequently, the upper part of the space had the higher absolute humidity than the lower part. The distribution pattern of the absolute humidity was very similar to that of room air temperature. Concerning the relative humidity, it had higher values near the supply opening, where the temperature was low, because relative humidity also depends on temperature. The relative humidity was distributed pretty uniformly from 45 to 50% through the whole room space.
Fig. 7. Relative humidity.
from the human body by convection, radiation, evaporation and respiration respectively. One of the main purposes of this paper was to clarify the characteristics of the heat loss from a standing human body, which has the metabolic heat production of 1.7 Met, in a stagnant environment. That scenario corresponded to one of the most common situations in an actual building space. Therefore from this study the engineer can obtain some general concept on how much heat is nor-
4.4. Wall surface temperature Fig. 8 shows the distribution of wall surface temperature. The adiabatic walls of the room gained heat from the human body by radiation, and then released the same quantity of heat to the air by convection. Thus the wall surface temperatures were generally approximately 0.38C higher than the room air temperature. The radiant heat transfer also occurred between the walls, due to the temperature dierence between the wall surfaces. That caused the trend of wall surface temperature to become uniform [3,13,14]. 4.5. Heat release characteristics from human body Fig. 9 illustrates the mean heat release quantity
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Fig. 8. Wall surface temperature (8C).
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Fig. 9. Heat release from human body (W/m2).
mally released from the human body through each route. As shown in Fig. 9, the human body released its metabolic heat production (1.7 Met) to the surround environment, 49.3 W (29.1 W/m2) by convection, 65.1 W (38.3 W/m2) by radiation, 41.3 W (24.3 W/m2) by evaporation and 14.8 W (8.7 W/m2) by respiration. As a total percentage of the entire heat released from the human body approximately 29.0% was by convection, 38.1% by radiation, 24.2% by evaporation and 8.7% by respiration under the conditions of this simulation. The human body released the most heat by radiation. This suggested that radiation played a signi®cant in¯uence on thermal sensation of the human body. 4.6. Heat balance between manikin and room walls Fig. 10 shows the heat balance between the manikin and the room walls. The ¯oor temperature was the lowest, generally 1.08C lower than that of the other walls (Fig. 8). Thus, the ¯oor gained the largest radiant heat 33.8 W in total from the human body as well as from the other walls. Conversely, the ceiling had the highest temperature. Therefore the ceiling released heat by radiation (5.5 W) to the other walls and gained heat from the air by convection. The side walls of the
Fig. 11. Surface temperature of human body.
room got less heat by radiation compared to the front and rear wall due to the smaller view factor between the human body (main radiation heat source) and the side walls. This can be easily understood from the location relationship since the human body faced the front wall. Concerning the two side walls, the radiant heat transfer rates were not equal to each other, although their surface temperatures were almost symmetrical (Fig. 8). That slight dierence was caused by the unsymmetrical distribution of the surface temperature of the human body. The right side of the human body facing the supply opening had lower skin temperature than the left side (Fig. 11). Thus the side wall with the supply opening gained slightly lower radiant heat from the human body than the opposite side wall with the exhaust opening.
4.7. Temperature of manikin skin surface
Fig. 10. Heat balance between human body and its environment.
Fig. 11 shows temperature distribution of the manikin skin surface. It generally ranged from 33.0 to 34.08C. It decreased below 29.08C at the right foot facing the supply opening, and increased above 34.08C at the neck and the shoulders. The previous experimental results [29] demonstrated a similar tendency of temperature distribution on the skin surface of a real human body. The mean skin surface temperature was calculated at 33.38C. This value was slightly lower than that of a human body in the state of physiological thermal neutrality (33.78C) with normal indoor activity [17].
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Fig. 12. Convective heat transfer characteristics of human body surface.
4.8. Convective heat transfer characteristics of manikin surface Fig. 12 illustrates the convective heat transfer rate and heat transfer coecient of the manikin skin surface. Both distribution patterns were similar to one another. The values were larger at the feet because of the thinner boundary layer at that location. They decreased with respect to the height direction of manikin. That kind of distribution corresponded to those of the vertical heated ¯at plate (heat and mass transfer book). The convective heat transfer rate ranged from 20.0 to 40.0 W/m2. The convective heat transfer coecient ranged from 3.0 to 4.0 W/(m2 K). It increased to 7.0 W/(m2 K) at the feet. The mean convective heat transfer coecient was determined to be 4.3 W/(m2 K). The results of mean value and distribution characteristics of the convective heat transfer coecient were in agreement with previous experiments [17,30,31]. 4.9. Radiant heat transfer characteristics of manikin surface Fig. 13(1) shows radiant heat transfer rate of the manikin surface. Neither the temperature dierence 3 More accurately, this concept is speci®ed as the plane radiative temperature, which is the average at each small plane on the body surface.
497
Fig. 13. Radiant heat transfer characteristics of human body surface.
among the room walls nor that at the manikin surface were signi®cantly large, thus the radiant heat transfer of the manikin surface ranged uniformly from 30.0 to 40.0 W/m2. The feet, however, had slightly smaller values due to the lower manikin surface temperature there. On average, the heat transfer by radiation (38.3 W/m2) was larger than that by convection (29.1 W/ m2). Fig. 13(2) shows the distribution of mean radiant temperature of the manikin surface. It was distributed almost uniformly from 27.0 to 28.08C.3 The left and right sides of the manikin had the low mean radiant temperature due to the large view factors of those parts towards the ¯oor, where temperature was low. 4.10. Evaporative heat transfer characteristics of manikin surface Fig. 14(1) shows the evaporative heat transfer rate of the body surface. It ranged from 20.0 to 30.0 W/m2. In this study it was assumed that the total (sensible+latent) heat loss rate was the same over the whole manikin surface. Consequently, the evaporative heat transfer rate decreased below 20.0 W/m2 at the feet, due to the large sensible heat transfer rate at that point. The evaporative heat transfer rate increased over 30.0 W/m2 at the shoulders. These results corresponded to previous experimental results [22]. Fig. 14(2) shows the evaporative heat transfer coecient of the manikin surface. The distribution characteristics were similar to that of the convective heat transfer coecient. Due to the thin boundary layer at
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Fig. 16. Blood ¯ow rate of human body. Fig. 14. Evaporative heat transfer characteristics of human body surface.
the feet, a large coecient value appeared there and decreased with respect to the height direction of the body. The evaporative heat transfer coecient generally ranged from 60.0 to 80.0 W/(m2 k Pa) over the manikin surface. The mean value was calculated as 70.2 W/(m2 k Pa). Using the ratio to mean convective heat transfer coecient 4.3 W/(m2 K), the Lewis ratio was obtained as 16.58C/k Pa, the exact same as the value recommended by ASHRAE [17].
4.11. Skin wettedness Fig. 15 shows the skin wettedness of the manikin surface. The evaporative heat transfer rate at the feet was low, causing the skin wettedness to also be low there at 0.06. That value (0.06) suggested that only diffusive evaporation occurred and that regulatory sweating was not generated at the feet in this environmental condition. The skin wettedness increased with respect to the height direction of the body. It reached the maximum value of over 0.18 at the shoulders. That distribution property corresponded to the actual situation of a real human body [22]. The mean value was 0.11. It also corresponded to that of a human body in thermal neutrality with the activity level of 1.7 Met. 4.12. Other physiological parameters of manikin The core temperature of the manikin was almost 36.98C everywhere (data not shown). It was almost the same as the neutral core temperature of 36.88C. Fig. 16 shows the skin blood ¯ow rate of the manikin. It generally ranged from 4.0 to 6.0 g/(s m2) over the manikin surface. The blood ¯ow rate was below 2.0 g/(s m2) at the feet. It increased above 7.0 g/(s m2) at the shoulders and the neck. This distribution property corresponded to the manikin surface temperature (Fig. 11).
5. Concluding remarks Fig. 15. Skin wettedness of human body.
A combined numerical simulation system was devel-
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Table A1 Derivation of boundary conditions of human body surface [11] Heat loss from respiration Qres Qres=0.014 M(34.0ÿTa)+1.73 10ÿ5M(5.87 103ÿPa)
(A1)
Heat balance equations for body core and skin layer Scr=(QmÿQres)ÿK(TcrÿTsk)ÿcp,blmbl(TcrÿTsk) Ssk=K(TcrÿTsk)+cp,blmbl(TcrÿTsk)ÿEskÿ(Qcv+Qr)
(A2) (A3)
Thermal neutrality for body core, skin layer, and whole body Tcr,n=36.88C Tsk,n=33.78C Tb,n=bnTsk,n+(1ÿbn)Tcr,n
(A4) (A5) (A6)
Thermo-regulatory control processes (vasomotor regulation and sweating) mbl=[(6.3+200WSIGcr)/(1+0.1CSIGsk)]/3600 mrsw=4.72 10ÿ5WSIGbexp(WSIGsk/10.7) b=0.042+0.745/(3600 mbl+0.585)
(A7) (A8) (A9)
Temperature signals WSIGcr=max((TcrÿTcr,n),0) CSIGsk=max((Tsk,nÿTsk),0) WSIGb=max((TbÿTb,n),0) WSIGsk=max((TskÿTsk,n),0) Tb=bTsk+(1ÿb )Tcr
(A10) (A11) (A12) (A13) (A14)
Boundary conditions for solving moisture transport equation Ersw=mrswhfg wrsw=Ersw/Emax Edif=(1ÿwrsw)0.06Emax w=wrsw+0.06(1ÿwrsw)=0.06+0.94Ersw/Emax Esk=wEmax Emax=ae(Psk,sÿPa,ref) msk=Esk/hfg
(A15) (A16) (A17) (A18) (A19) (A20) (A21)
Boundary conditions for coupled simulation of heat convection and radiation Qt=QmÿQresÿEsk
(A22)
oped for predicting air¯ow, moisture transport, and thermal radiation based on a human thermo-physiological model. That system made it possible to investigate precisely the distributions of both sensible and latent heat transfer characteristics at the skin surface of the human body. The two-node model was used here. It was originally developed for applying to the whole body heat budget. In its original concept it could not be applied to analyze the local heat transfer as was carried out in this study. However, when adapting it locally to body surface, the obtained heat transfer characteristics of the body corresponded with the actual phenomena of the real human body. The use of the two-node model locally at the body surface seemed tolerable in such analyses. The multi-node model will be further examined at the next stage. Thermal sensation indices such as SET and PMV can be reported based on the results of this study. Human's thermal sensation thus can be further predicted precisely by means of the combined numerical prediction system developed in this study.
Appendix A Boundary conditions of body surface were derived based on the two-node model. Table A1 shows the setup of the equations. The two-node model [10,11] represented the body as two concentric cylinders, i.e., the inner cylinder referred to the body core and the outer cylinder referred to the skin layer. The metabolic heat production at the core was released to the environment by two routes. The major one was to transfer heat to the skin by blood ¯ow and heat conduction, and to be released from the skin to the environment by convection, radiation and evaporation. The minor one was a direct release to the environment through respiration (Eq. A1). As shown in Eqs. (A2) and (A3), two heat balance equations for the body core and the skin layer were built up. Here the steady state was assumed; thus the rates of heat storage, Scr and Ssk, were regarded as zero. When the body was in the state of thermal neutrality physiologically, the mean temperatures of the core node Tcr,n, the skin layer Tsk,n, and the entire body
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Tb,n were at their neutral values (Eqs. (A4)±(A6)). If the temperature deviated from neutrality, the thermoregulatory control processes (vasomotor regulation, sweating, and shivering) occurred. These processes were simulated through the temperature signals as shown in Eqs. (A7) and (A8). The temperature signals were speci®ed in Eqs. from (A10) to (A13). The mean body temperature Tb was calculated from Eq. (A14). The actual ratio of the skin mass to the whole body mass b was calculated from Eq. (A9), because of its dependency on the blood ¯ow rate. The evaporative heat loss by regulatory sweating Ersw and the skin wettedness due to regulatory sweating wrsw were calculated from Eqs. (A15) and (A16), respectively, by the speci®ed regulatory sweat rate mrsw. With no regulatory sweating, the skin wettedness due to diusion was 0.06 for normal conditions. Then the diusion evaporative heat loss Edif was calculated from Eq. (A17). The total evaporative heat loss from skin Esk was shown in Eq. (A19). The total sweat rate generated from skin msk was simply calculated from Eq. (A21). That value became the boundary condition of the body surface for solving the moisture transport equation. The sensible heat loss from skin Qt was derived as Eq. (A22). It became the boundary condition of the human body surface for coupled simulation of heat convection and radiation. References [1] Murakami S. Prediction, analysis and design for indoor climate in large enclosures. ROOMVENT'92 1992;1:1±30. [2] Kato S, Murakami S, Shoya S, Hanyu F, Zeng J. CFD analysis of ¯ow and temperature ®elds in atrium with ceiling height of 130 m. ASHRAE Transactions 1994;95(2). [3] Murakami S, Kato S, Zeng J. Flow and temperature ®elds around human body with various room air distribution, CFD study on computational thermal manikin (Part 1). ASHRAE Transactions 1997;103(1):3±15. [4] Murakami S, Kato S, Zeng J. Numerical simulation of contaminant distribution around a modeled human body, CFD study on computational thermal manikin (Part 2). ASHRAE Transactions 1998;104(2). [5] Chen Q. Computational ¯uid dynamics for HVAC: successes and failures. ASHRAE Transactions 1997;103(1):178±87. [6] Murakami S, Kato S, Kondo Y, Takahashi Y, Choi D. Numerical study on thermal environment in air-conditioned room by means of coupled simulation of convective and radiative heat transport, method for coupling convective simulation and radiative simulation (Part 1). Transactions of the Society of Heating, Air-Conditioning and Sanitary Engineers of Japan (SHASE) 1995;57:105±16 [in Japanese]. [7] Murakami S, Kato S, Choi D, Kobayashi H, Omori T. Numerical study on thermal environment in air-conditioned room by means of coupled simulation of convective and radiative heat transport, accuracy of shape factor calculation by modi®ed Monte Carlo method and its application for a room with complex geometry (Part 2). SHASE Transactions 1995;59:95±104 [in Japanese]. [8] Murakami S, Kato S, Zeng J. Coupled simulation of convective and radiant heat transfer around standing human body, study
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