Modeling Human Thermoregulation and Comfort. CES Seminar

Transcription

1 Modeling Human Thermoregulation and Comfort CES Seminar

2 Contents 1 Introduction Modeling thermal human manikin Thermal neutrality Human heat balance equation Bioheat equation Thermophysiological model Passive system Active system Thermal comfort models Fanger ISO Zhang Simulation Results Fanger ISO Zhang Conclusion Literature... 26

3 1 Introduction 1 1 Introduction The objective of this work is to give an overview about the modeling of human thermoregulation and comfort. For this, basic concepts and equations regarding the modeling of a virtual thermal manikin, including the thermoregulation system, were presented. Moreover, three different models for the evaluation of thermal comfort were explained. In conclusion, a test case was simulated with the software THESEUS-FE in order to provide results for the analysis of the thermoregulation mechanisms of the virtual manikin and for the comparison between the thermal comfort models as well.

4 2 Modeling thermal human manikin 2 2 Modeling thermal human manikin In order to model a virtual thermal manikin, some concepts and mechanisms of the human body should be taken into consideration: the meaning of thermal neutrality, the human heat balance equation, the thermoregulatory system, among others. 2.1 Thermal neutrality Thermal neutrality is known as the state of the human body in which no thermoregulatory mechanism is activated in order to keep the organism in thermal balance. This state results from the balance between the body heat losses to the environment and the basal body heat production. At this state, the average skin temperature and the body core temperature are 33.5 C and 37 C, respectively. [1] [2] 2.2 Human heat balance equation The heat balance equation for the human body describes the heat transfer between the body and the environment, as well as inside the body itself. The main term are the heat generation inside the body, heat transfer and heat storage. [1] The heat released by the body ( ) is the result of the difference between the energy generated by the metabolic rate () and the energy used by the body to do mechanical work (). The heat transfer between the body and the environment and inside the body occurs by conduction (), convection (), radiation () and evaporation / respiration (). The resulting heat of the balance is defined as heat storage (). The heat storage is used to identify how the body temperature changes. If the body gains heat, i.e., the body temperature rises, the heat storage is positive ( > 0). If the body losses heat, i.e., the body temperature falls, the heat storage is negative ( < 0). The thermal neutrality state of the human body, cited on Chapter 2.1., occurs if the heat storage is zero ( = 0). [1]

5 2 Modeling thermal human manikin 3 = Eq. 2-1 Fig. 2-1: Schematic energy exchanges of the human body [3] 2.3 Bioheat equation The bioheat equation (Eq. 2-2) is considered the state of the art for the modeling of heat transport in living tissues. It is based on Fourier s law for heating conduction. Moreover, it considers the moving blood as isotropic heat source and the metabolic heat production. [4] [5] (!.#) %&'% + ( ) )*+) +, *+.- *+.. *+.(# *+, #) + *+& =,. 0# 01 Eq. 2-2

6 2 Modeling thermal human manikin 4 The first term corresponds to the Fourier s law for heating conduction. The second term is the heat generated by the metabolism. The third term represents the heat generated by the blood flow. The last term on the right side of the equation corresponds to the heat storage of the Eq. 2-1, cited on Chapter 2.2. [4] [5] 2.4 Thermophysiological model In order to model the thermophysiology of the human body, the model can be divided into a controlled passive system and a controlling active system, as explained in more detail in the following chapters Passive system The passive system is responsible for calculating the heat balance of the human body. Due to the complexity of the human body geometry, the body parts should be approximated to more simple shapes in order to facilitate the calculation of the heat exchange within the body and between the body and the environment. The head was approximated by a half concentric sphere, while all other body parts were approximated to concentric cylinders. These concentric shapes were made of layers representing the body layers: bone, muscle, fat and skin, as shown in Fig [5]

7 2 Modeling thermal human manikin 5 Fig. 2-2: Layers of the virtual manikin [5] The heat transfer within the body layers and between the body and the environment can occur by conduction, convection, radiation, contact and evaporation, as shown in Fig [5] Fig. 2-3: Heat transfer within segment layers and between the segment and the environment [5]

8 2 Modeling thermal human manikin 6 The bioheat equation described on Chapter 2.3. is used to model the heat transport in living tissues. The thermoregulation system is based on this equation, which was formulated for spherical and polar coordinates as shown on Eq In order to calculate the heat transfer on cylinders, the (-) is set to 1, while for spheres, it should be set to 2. The variables for metabolism (( ) ) and rate of blood flow (- *+ ) are controlled by the active system. [5] 23 0²# 05² + - 0# %&'% =,. 0# 01 + ( ) )*+) +, *+.- *+.. *+.(# *+, #) + *+& Eq Active system As cited on Chapter 2.1., the body has thermoregulatory mechanisms that, if necessary, are activated in order to keep the organism in thermal balance. This is known as the active system, which is controlled by the hypothalamus and is responsible for the regulation of the body temperatures through four regulatory responses: vasoconstriction, shivering, vasodilation and sweating. Through these regulatory responses, the active system controls the heat transfer within the passive system. The governing factors of the thermoregulatory system are the hypothalamus temperature (# 7 ), the skin temperature (# 8 ) and the rate of change of skin temperature (9# 8, 91), as shown in Fig [5]

9 2 Modeling thermal human manikin 7 Fig. 2-4: Active system [5] The active system is expressed than as a state function (Eq. 2-4), which depends on these three state variables: hypothalamus temperature (# 7 ), mean skin temperature (# 8,) ) and the derivation of the mean skin temperature (0# 8,) 01). It is possible to detect if a regulatory response is active based on these three state variables. For this the following functions are used: global vasoconstriction (Eq. 2-5), global shivering (Eq. 2-6), global vasodilatation (Eq. 2-7) and global sweating (Eq. 2-8). One of these responses are activated if its value is greater than zero (; > 0), otherwise it is deactivated. [5] ; = ;<# 7,# 8,),0# 8,) 01= 0 Eq. 2-4

10 2 Modeling thermal human manikin 8 Global vasoconstriction function:? = 35.[tanh<0,29. # 8,) + 1,11= 1]. # 8,) 7,7. # # 8,). 0# 8,) ) 01 MN OP QR,S O T N P QR,S T N Eq. 2-5 Global shivering function: h = 10.Vtanh<0,51. # 8,) + 4,19= 1X. # 8,) 27,5. # 7 28,2 + 1,9. # 8,). 0# 8,) 01 MN OP QR,S O T N P QR,S T N Eq. 2-6 Global vasodilatation function: Z[ = 16.[tanh<1,92. # 8,) 2,53= + 1]. # 8,) + 30.[tanh<3,51. # 7 1,48= + 1]. # 7 Eq. 2-7 Global sweating function: - = [0,65.tanh<0,82. # 8,) 0,47= + 1,15]. # 8,) + [5,6.tanh<3,14. # 7 1,83= + 6,4]. # 7 Eq. 2-8

11 3 Thermal comfort models 9 3 Thermal comfort models Thermal sensation and comfort models are used to translate thermophysiological and environmental information into perceived comfort sensation for people. There are several models available to evaluate the thermal comfort of a person and each model has it owns particularities. In general, thermal comfort models can be categorized as Global and/or Local models, as well as Static and/or Dynamic models. Global models evaluates the thermal comfort of the body as a whole, while Local models is analyses the distinct parts of the human body separately. On the contrary to Dynamic models, Static models don t take into account the change of conditions with the time. For this work, three thermal sensation and comfort models were presented: Fanger (1970), EN ISO (2006) and Zhang (2003). Fanger (1970) EN ISO (2006) Zhang (2003) Global Local Static Dynamic Fig. 3-1: Overview thermal comfort models 3.1 Fanger Based on experiments made with 1300 human subjects, Fanger developed an empirical function to evaluate the thermal sensation of a large group of people. This empirical function was named Predicted Mean Vote (PMV), Eq. 3-1, and takes into consideration the heat balance of the human balance described on Chapter 2.2. Therefore, the input information for the PMV function are the clothing factor (] %+ ), convective heat transfer coefficient (h % ), clothing insulation (^%+ ) in [clo], metabolic rate () in [W/m²], vapor pressure of air (_ ) in [kpa], clothing thermal insulation

12 3 Thermal comfort models 10 ( %+ ), air temperature (1 ) in [ C], surface temperature of clothing (1 %+ ) in [ C], mean radiant temperature (1 ) in [ C], air velocity (`) in [m/s], and external work (), as shown in Eq. 3-1, Eq. 3-2, Eq. 3-3, Eq. 3-4 and Eq [1] a` = [0,303.b cn,nde.f + 0,028]g( ) 3,96. ch.] %+.[(1 % ) i ( ) i ] ] %+.h %.(1 %+ 1 ) 3,05.[5,73 0,007( ) _ ] Eq ,42.[( ) 58,15] 0,0173..(5,87 _ ) 0,0014..(34 1 )j With 1,0 + 0,2.^%+ ] %+ = k Eq ,05+0,1.^%+ 1 %+ = 35,7 0,0275.( ) %+.g( ) 3,05.[5,73 0,007.( ) _ ] 0,42.[( ) 58,15] 0,0173..(5,87 _ ) Eq ,0014..(34 1 ) %+ = 0,155.^%+ Eq. 3-4 h % = 12,1.`N.l Eq. 3-5 Based on the Predicted Mean Vote (PMV), Fanger developed a function to predict the percentage of people who would be dissatisfied with the thermal condition of the environment. This function is linearly related to the PMV function and is known as Predicted Percentage of Dissatisfied (PPD), Eq [1]

13 3 Thermal comfort models 11 aaz = b [c<n,ddld.mfno pn,qrst.mfn u =] Eq. 3-6 The correlation between the Predicted Mean Vote and the Predicted Percentage of Dissatisfied was represented on Fig [8] Fig. 3-1: Correlation between PMV and PPD [6] 3.2 ISO The ISO evaluates thermal comfort based on a so-called equivalent temperature (Eq. 3-6). The equivalent temperature is defined as (the) temperature of a homogeneous space, with mean radiant temperature equal to air temperature and zero air velocity, in which a person exchanges the same heat loss by convection and radiation as in the actual conditions under assessment. It is calculated based on the heat exchange between the environment and the human body by taking into consideration the heat transfer (v) by convection () and radiation (), as shown in Eq. 3-7, Eq. 3-8 and Eq [7]

14 3 Thermal comfort models 12 1 w = 1 8 v h %+ Eq. 3-6 v = + Eq. 3-7 = h.(1 8 1 x) Eq. 3-8 = h %.(1 8 1 ) Eq. 3-9 This ISO standard evaluates the equivalent temperature for multiple segments of the body, as shown in Fig The letter (() corresponds the value average value for the whole body. [7] q p o n m l k j i h g f e d c b a Whole body Scalp Face Chest Upper back Left upper arm Right upper arm Left lower arm Right lower arm Left hand Right hand Left thigh Right thigh Left calf Right calf Left foot Right foot Fig. 3-2: Body parts for ISO s model [7] To facilitate the analysis of the equivalent temperatures, the ISO standard uses the comfort zones for summer and winter conditions separately. For the summer comfort zones (Fig. 3-3), a clothing factor of 0.6 [clo] was assumed, while for

15 3 Thermal comfort models 13 the winter comfort zones (Fig. 3-4), the clothing factor was 1.0 [clo]. The zone 1 and 2 correspond to the too cold and cold but comfortable zones, respectively. The zone 3 neutral is the zone corresponding to thermal neutrality, cited on Chapter 2.1. The zones 4 and 5 are, respectively, the zones warm but comfortable and too warm. [7] Fig. 3-3: Summer comfort zones [7] Fig. 3-4: Winter comfort zones [7]

16 3 Thermal comfort models Zhang Zhang developed models to predict local and global thermal sensation, as well as local and global thermal comfort. The models are based on the following input information: skin temperature (# 8,+%+ ) and core temperature (# % ). The rates of change of skin temperature, rates of change of core temperature, perceptions of local sensation ( +%+ ), perceptions of local comfort ( +%+ ), perceptions of global sensation ( y++ ) and perceptions of global comfort ( y++ ) are also calculated in order to be evaluate the thermal sensation and thermal comfort (Fig. 3-5). [8] To evaluate the thermal sensation, a nine-point scale was used: very cold (-4), cold (-3), cool (-2), slightly cool (-1), neutral (0), slightly warm (+1), warm (+2), hot (+3) and very hot (+4). Analogous, a scale was used to evaluate the thermal comfort: very uncomfortable (-4), uncomfortable (-2), just comfortable (0), comfortable (+2) and very comfortable (+4). [8] Fig. 3-5: Zhang s framework for local thermal comfort prediction [5]

17 4 Simulation 15 4 Simulation In order to evaluate the thermal comfort of a virtual manikin based on the three comfort models cited on Chapter 3, the software THESEUS-FE was used. THESEUS-FE is a thermal analysis tool, which is based on the Finite Element Method (FEM) and is capable to calculate 3D heat exchange by convection, conduction and (shot and long-wave) radiation. THESEUS-FE has also an integrated thermal manikin, namely FIALA-FE. The FIALA-FE manikin simulates the thermophysiology of the human body through a virtual thermal manikin. The virtual manikin is able to calculate the thermal responses of the human body, such as vasoconstriction, vasodilatation, shivering, sweating, evaporation, respiration and metabolic rate. The test case consists of a virtual manikin positioned inside a box, as shown in Fig The initial air temperature was set to -10 C, with air velocity around 0.1 m/s and relative air humidity at 10%. The walls on the left and on the right sides of the manikin were set to a constant temperature of 100 C. The walls in front of and on the back of the manikin had an initial temperature of -10 C. The initial mean skin temperature was around 34.4 C, while the initial hypothalamus temperature was C. The metabolic rate of the manikin was set to a constant value of 1.2 met, with a heat production of W. The simulation time was 180 seconds. The idea behind the test case was to test if model can rapidly capture temperature changes, and as a result, correctly simulate the thermoregulation actions of the human body.

18 4 Simulation 16 Fig. 4-1: Virtual manikin inside a box 4.1 Results During the 180 seconds of the simulation, the hypothalamus temperature decreased slightly from C to C, as shown on Fig The temperature variation is small but decisive for activation of the thermoregulation mechanism of the body, as cited on Chapter The small variation of the hypothalamus temperature was expected, as this is the most important temperature of the body and should be keep around its temperature in thermal neutrality.

19 4 Simulation 17 Fig. 4-2: Hypothalamus temperature during 180 seconds The mean skin temperature is the average value of all skin temperatures. For the first 25 seconds, this temperature decreased rapidly from C to 34.0 C, as shown in Fig This was expected due to the cold initial temperature of the air. The mean skin temperature gradually rose from 34.0 C to 34.1 C because of the influence of the high temperatures of the wall on both sides of the virtual manikin. The temperature variation was also small as the simulation run for only 180 seconds and because this value is an average skin temperature of all body parts. Fig. 4-3: Mean skin temperature during 180 seconds The average air temperature (Fig. 4-4) increased rapidly in the first 25 seconds, more precisely from -10 C to 18 C. After that, the air temperature rose more slowly until around 30 C. The rapidly decrease of the mean skin temperature for the first 25 seconds and the slowly increase afterwards is related to the average air temperature and to the thermoregulation mechanism of the body. The mean skin temperature decreased rapidly while the air temperature was low. After that, when the air

20 4 Simulation 18 temperature was around 18 C, the mean skin started heating up slowly. The heating of the skin is related to the thermoregulation mechanisms of the body, which will be explained later on this chapter, as well as to the small influence of the air temperature after 25 seconds and, of course, due to the high wall temperatures, which heated the air inside the box. The equivalent temperature for the whole body is also presented on Fig It shows the correlation between the average air temperature and the equivalent temperature of the manikin. Fig. 4-4: Air temperature and equivalent temperature during 180 seconds Due to the low initial air temperature, the thermal condition inside the box for the first seconds was identified as too cold for the virtual manikin. The high wall temperature was not enough to heat the air temperature to a comfortable value for the virtual manikin. Thereby, thermoregulation mechanisms of the body were activated in order to prevent the body to lose too much heat to the environment. For the first seconds, the shivering and the vasoconstriction, both cited on Chapter , were activated. This behaviour was expected, as these are the mechanisms used by the human body to avoid heat loss if the body temperatures are too low. The shivering mechanism was activated in the first 8 seconds, while the vasoconstriction was activated until around the first 20 seconds of the simulation, as shown in Fig. 4-5 and Fig. 4-6, respectively. This behaviour corresponds to the real thermoregulation system of the body. If the environment is cold, the vasoconstriction mechanisms is activated.

21 4 Simulation 19 Moreover, if the environment is too cold, the vasoconstriction is however not enough to avoid the heat loss from the body. In this case, the human body also activates the shivering, in order to generate heat inside the muscles. Fig. 4-5: Shivering activated during the first 8 seconds Fig. 4-6: Vasoconstriction activated during the first 20 seconds

22 4 Simulation Fanger The results for Fanger s Predicted Mean Vote is shown in Fig For the first 40 seconds, this model evaluated the thermal comfort as cold. Afterwards, the thermal comfort change progressively from too cold to cool, then to slightly cool and almost reached the vote neutral after around 150 seconds. This condition is the thermal neutrality, cited on Chapter 2.1. Fig. 4-7: PMV values during 180 seconds As explained on Chapter 3.1., the PPD value describes predict the percentage of people who would be dissatisfied with the thermal condition of the environment and is linearly related to the PMV value. The correlation of both results is seen by comparing the behaviour of both curves. The PPD (Fig. 4-8) value was 100% of dissatisfied for the first 40 seconds, then this value decreased gradually until it reached the lowest possible PPD value of 5% after 150 seconds. It means that most of the people would be satisfied with the environment conditions after this time, or in other words, they would be reached the thermal neutrality condition.

23 4 Simulation 21 Fig. 4-8: PPD values during 180 seconds ISO The local thermal comfort values based on ISO s model is shown in Fig The dark and light blue colors represent the too cold and cold but comfortable values. The green color corresponds to the neutral condition, while the yellow and red colors represent the warm but comfortable and too warm votes. It is important to point out that these values are based directly on the equivalent temperature and that they are not representing the skin temperatures. At the beginning of the simulation, the whole body was evaluated as too cold due to the low initial temperatures, except for the head, which was evaluated as warm but comfortable. The head is normally kept warm by the body in order to maintain the hypothalamus temperature at around 36.9 C. Then after 15 seconds, the torso and the head started heating up faster than the other body parts, reaching the neutral and warm but comfortable votes. This behaviour was expected, as these are known as the most important body parts to keep warm and, therefore, are the first ones to be heated up by the blood flow. Starting for this points, the other body parts heated up gradually until the torso reached the vote too warm, while the other body parts

24 4 Simulation 22 were evaluated as warm but comfortable after 180 seconds. An exception are the feet, which were evaluated as too cold during the whole time. Fig. 4-9: Local thermal comfort values (ISO ) during 180 seconds The average values for the thermal comfort of the whole body is shown in Fig In the first 35 seconds, the thermal comfort was as too cold. After that, for the next 15 seconds, it was evaluated as cold but comfortable. The overall thermal comfort was valued as neutral after 60 seconds, diverging with the results from Fanger s model, which was valued as neutral after 150 seconds. The results based on the ISO standard reached after just 100 seconds a higher scale than Fanger s model, evaluating the thermal comfort after this time as warm but comfortable, while the highest vote reached by Fanger s model was just neutral. Fig. 4-10: Global thermal comfort values (ISO ) during 180 seconds

25 4 Simulation Zhang The local thermal comfort values based on Zhang s model is shown in Fig The dark and light blue colors represent the very uncomfortable and uncomfortable values. The green color corresponds to the just comfortable condition, while the yellow and red colors represent the comfortable and very comfortable votes. It is important to point out that these values corresponds to the thermal comfort votes and that they are not representing the skin temperatures. At the beginning of the simulation, the whole body was evaluated as very uncomfortable. This is in line with the results from ISO s model, except for the head, which was evaluated as more uncomfortable by Zhang s than by ISO s model. Another similarity with ISO s model is that the head and torso reached comfortable conditions faster than the other body parts. A remarkable difference between both models are the results for the feet. Zhang s model evaluated the feet directly after 15 seconds as just comfortable, while ISO s model evaluated the feet condition as too cold during the whole time. Fig. 4-11: Local thermal comfort values (Zhang) during 180 seconds

26 4 Simulation 24 The average values for the thermal comfort of the whole body is shown in Fig In the first few seconds, the vote changed rapidly from very uncomfortable to uncomfortable. After only 25 seconds the overall thermal comfort was evaluated as just comfortable. Comparing this with the results from Fanger s and ISO s models shows a notable discrepancy. The evaluation of Zhang s model reached the neutral state just after 60 seconds, while Fanger s model reached this condition almost at the end of the simulation around 150 seconds. Zhang s model evaluated the state at the end of the simulation near the neutral zone with slightly higher votes. In comparison to Fanger s and ISO s model, the results of Zhang s model lies between both models results. Fig. 4-12: Global thermal comfort values (Zhang) during 180 seconds

27 5 Conclusion 25 5 Conclusion The thermophysiological model was able to reproduce the expected thermoregulation mechanisms of the human body. The correct reproduction of the thermoregulation system and, as a result, the correct prediction of the body temperatures are crucial for the evaluation of the thermal comfort. Although the three thermal comfort models shown some similarities regards the results, remarkable discrepancies on the results were found. Thereby, a more detailed comparison of the thermal comfort models is required.

28 6 Literature 26 6 Literature [1] PARSONS, K. Human Thermal Environments The Effects of Hot, Moderate, and Cold Environments on Human Health, Comfort, and Performance CRC Press, Boca Raton (USA), 2014 [2] HOURDAS, Y. Human Body Temperature Its Measurement and Regulation Springer, New York (USA), 1982 [3] FABBRI, K. Indoor Thermal Comfort Perception A Questionnarie Approach Focusing on Children Springer, Cham (Switzerland), 2015 [4] LEONDES, C. Biomechanical Systems Techniques and Applications CRC Press, Boca Raton (USA), 2001 [5] P+Z Engineering GmbH THESEUS-FE Theory Manual Version P+Z Engineering GmbH, München (Germany), 2016 [6] ANKERSMIT, B. Managing Indoor Climate Risks in Museums Springer, Cham (Switzerland), 2016 [7] ISO ISO Ergonomics of the thermal environment - Evaluation of thermal environments in vehicles - Part 2: Determination of equivalent temperature ISO, Geneva (Switzerland), 2006 [8] ZHANG, H. Human thermal sensation and comfort in transient and non-uniform thermal environments University of California, Berkeley (USA), 2003