Improvement of the Stolwijk model with regard to clothing,thermal sensation and skin temperature

Abstract

BACKGROUND: The original Stolwijk model is not equipped with clothing, thermal sensation, comfort indices, individual characteristics and performance loss models.

OBJECTIVE: This study attempts to modify the model to include clothing, thermal sensation as well as the calculation of the percentage of dissatisfied as a result of general discomfort. The model is useful for the evaluation of thermal comfort in the built environment by professionals.

METHODS: Methods described in literature with regard of clothing, the research of Fiala as well as some in the literature recommended and validated adjustments, to improve the simulation of the skin temperature per body segment, are implemented in the here assembled Stolwijk computer model. Finally, for verification of the above adjustments, the model was compared with experiments conducted in the field of thermal sensation at various levels of temperature change.

RESULTS: By improving the simulation of the skin temperature per body segment and by adding clothing and thermal sensation, suitable for the assessment of steady state and transient thermal conditions, and fixed with this the percentage of dissatisfied, the scope of the Stolwijk model has become larger than it was before.

CONCLUSION: On the basis of the calculations and the experimental results, it was concluded that the adjusted Stolwijk model was suitable for the simulation of the thermal sensation under steady state and transient thermal conditions.

Keywords

Mathematical human modelling transient thermal sensation

1 Introduction

There has been a growing demand from research and the industry for detailed models predicting human thermo physiological responses. Thermophysiological models are necessary for the design of the indoor thermal climate.

Stolwijk [1] developed a thermophysiological human model which today is still the basis and inspiration for many other thermophysiological human models. Some later on developed thermophysiological human models are usually tailored to specific applications, for instance the cold side of the comfortzone [21] or Chinese people [13]. Often the source code of the computer programs of these models are not released and the computer programs are not made available for the professional practice. The Stolwijk model was developed for the NASA (National Aeronautics and Space Administration) with the aim of creating a mathematical model to simulate the thermoregulation of a human, under dynamic dynamic conditions. This model simulated the physiological responses of people in different environmental conditions. The default of this model was a naked male, with a height of 1.72 m and a weight of 74.4 kg. The Stolwijk model as compared to the Gagge model [2] was more extensive in scope, e.g. because the heat balance of the body was divided into the head, the trunk, arms, hands, legs and feet. In addition, the aforementioned body parts were divided into a core, a muscle layer, a fat layer and a skin layer. NASA made the Stolwijk model available for the professional practice [1], and is well described in the literature [3 –5] and extensively validated [1 , 7]. Because the body was devided into several body parts, one would expect that the Stolwijk model basically is suitable for the evaluation of the general and the local discomfort. The original Stolwijk model however was not equipped with clothing, thermal sensation, comfort indices, individual characteristics, and performance loss models. The model is made available by NASA and still used for research in the industry and research community by among others NASA [22], the Biophysics and Biomedical Modelling Division US Army Research Institute of Environmental Medicine [23] and universities [7 , 25].

This study attempts to modify the model to include clothing, thermal sensation as well as the calculation of the percentage of dissatisfied as a result of the general discomfort; so the model is useful for the evaluation of thermal comfort in the built environment. Furthermore some in the literature recommended and validated adjustments, to improve the simulation of the skin temperature per body segment, are implemented in this reconfigured Stolwijk model. Finally, for verification of the above adjustments, the model is compared with experiments conducted in the field of thermal sensation at various forms of temperature change.

2 Stolwijk model

2.1 Passive part

The passive part of the model consists of five cylinders and a sphere with adjusted dimensions (the dimensions are determined by measurements on subjects) (see Fig. 1). The cylinders represent the trunk, arms, hands, legs and feet, the sphere represents the head. Each element consists of four concentric layers or compartments that comprise the core, the muscle tissue, the fat and the skin layers. The model also contains a central blood compartment, which represents the large arteries and veins. In this compartment heat is exchanged with the other compartments by convective heat distribution (this occurs when blood flows to the other compartments). The model assumes that the body is symmetrically built up; the legs, the arms, the feet and the hands are represented by one cylinder each. The total passive system consists of 25 nodes: five cylinders and a sphere, each consisting four layers, and one central blood compartment.

2.2 Active part

The active part of the model is the thermoregulation system (see Fig. 2) which perceives the ambient temperature and consists of an integrating and regulatory system. It is a simplified representation of the actual human thermoregulation system and is based on set point values. The set point value is basically the temperature for each node that a node would have in a neutral condition. If the value in a node is different from this set point value then the regulatory mechanisms are used.

3 Clothing

The original Stolwijk model was not equipped with clothing. In order for the model to be useful in the evaluation of the thermal comfort within the built environment it was necessary that clothing be included in the assessment.

For that reason, the Stolwijk model, for all body segments, was modified with the following equations:

Fcl_i = 1/(1+0,155*(α_c,i+α_r,i)*clo_i*1,163)

Facl = 1+0,15* clo_i

clo_e = clo_i – (Facl-1)/(0,155*Facl*(α_c,i+α_r,i))

Fpcl_i = 1/(1+0,143* α_c,i*SQR(v_air/0,1)*clo_e*1,163)

Lr_i = 2,02*(T_sk,i+273,15)/273,15

Emax_i = (Pskin_i-Pair)*Lr* α_c,i* SQR(v_air/0,1)* Fpcl_i*S_i

HF_sk,i = Q_sk,i – BC_sk,i – E_sk,i + TD_fat,i – (α_r,i*Fcl_i*(T_sk,i-T_mrt) - α_c,i*Fcl_i*SQR(v_air/0,1)*(T_sk,i - T_air))*S_i

Herein is:

i = number segment [–]

Fcl = Burton clothing efficiency factor [–]

Fpcl = Nishi permeation efficiency factor for clothing [–]

Emax = maximum evaporative heat loss [kcal/h]

α_c = convective heat transfer coefficient [kcal/(m²·h·K)]

clo_i = intrinsic clothing resistance [clo]

clo_e = effective clothing resistance [clo]

Pskin = saturated water vapor pressure at skin temperature [mmHg]

Pair = vapor pressure in environment [mmHg]

v_air = air velocity [m/s]

HF_sk = rate of heat flow into or from segment [kcal/h]

Q_sk = total metabolic heat production [kcal/h]

BC_sk = convective heat transfer between central blood and segment [kcal/h]

E_sk = total evaporative heat

TD_fat = thermal conductance between fat and skin [kcal/h]

α_r = radiant heat transfer coëfficiënt [kcal/(m²·h·K)]

T_sk = skin temperature [°C]

T_mrt = mean radiant temperature [°C]

T_air = air temperature [°C]

S = surface body part [m²]

Lr = Lewis relation; ratio of the evaporative heat transfer coefficient to the convective heat transfer coefficient [°C/mmHg].

In this study the calculation of the clo value was executed with a for this study assembled computer program, based on a model of J. Lotens. It calculated the clothing insulation values for a four cylindrical model of the human body. The model was covered with a clothing layer except for head and hands [8].

4 Dynamic thermal sensation

In 1998 Fiala also developed a thermophysiological model [9], based on the Stolwijk model. This model assumes a standard male weighing 73.5 kg, a body fat percentage of 14%, a Dubois area of 1.9 m² and a basal metabolic rate of 87, 1 Watt. The model of Fiala is split into passive and active parts, the core temperature, the mean skin temperature and the rate at which the mean skin temperature changes are the parameters which control the regulatory mechanisms. The control principle is equivalent to the control system of the Stolwijk model; if the core temperature or the mean skin temperature differs from the set point values than the regulatory mechanisms are in operation [18].

In the Fiala model an equation is included to predict the thermal sensation under dynamic conditions, the so called dynamic thermal sensation (DTS), based on the simulated core temperature and the mean skin temperature. The equation for predicting the thermal sensation is based on a large number of independent experiments. Using a multivariate analysis it was found that the mean skin temperature, the core temperature and the rate at which the mean skin temperature changes are the parameters affecting the thermal sensation under dynamic conditions. The thermal sensation was assessed on the basis of the ASHRAE seven-point scale [10]. Experiments showed that the predicted DTS and the PMV (Predicted Mean Vote), according to (NEN-EN-)ISO-7730 [11] were in agreement. In the studies of Fiala two versions of the dynamic thermal sensation were published. Both versions are included in the following modified Stolwijk model:

4.1 DTS-version 1 [9]

DTS1 = 3 * tanh(f_sk + φ + ψ) [-]

Where:

$\begin{matrix} f_{sk} = 1, 026 * Δ T_{sk, m} & [-] & ; for Δ T_{sk, m} > 0 \end{matrix}$

$\begin{matrix} f_{sk} = 0, 298 * Δ T_{sk, m} & [-] & ; for Δ T_{sk, m} < 0 \end{matrix}$

$\begin{matrix} Δ T_{sk, m} = (T_{mean skin} - 34, 4) & [K] \end{matrix}$

$\begin{matrix} φ = 6, 662 * exp (- 0, 565 / Δ T_{hy}) * \end{matrix}$ $\begin{matrix} exp (- 7, 634 / (5 - Δ T_{sk, m})) \\ [-]; φ = 0 when Δ T_{hy} \leq 0 or Δ T_{sk, m} \geq 5 \end{matrix}$

$\begin{matrix} Δ T_{hy} = (T_{hypothalamic} - 37, 0) & [K] \end{matrix}$

$\begin{matrix} ψ = (τ_{-} + τ_{-}) / (1 + φ) & [-] \end{matrix}$

$\begin{matrix} τ_{-} = 0, 114 * {dT}_{sk, m} / dt & [-] & ; for {dT}_{sk, m} / dt < 0 \end{matrix}$

$\begin{matrix} τ_{+} = 0, 137 * ({dT}_{sk, m} / dt)_{max} . \end{matrix}$ $\begin{matrix} exp (- 0, 681 * Δ t) [-]; for {dT}_{sk, m} / dt > 0 \end{matrix}$

$\begin{matrix} Δ t = t - t_{0} & [h] \end{matrix}$

$\begin{matrix} t_{0} = time of occurrence of highest \\ rate {dT}_{sk, m} / dt [h] \end{matrix}$

4.2 DTS-version 2 [12]

DTS2 = 3 * tanh(f_sk + φ + ψ) [-]

Where:

$\begin{matrix} f_{sk} = 1, 08 * Δ T_{sk, m} & [-] & ; for Δ T_{sk, m} > 0 \end{matrix}$

$\begin{matrix} f_{sk} = 0, 30 * Δ T_{sk, m} & [-] & ; for Δ T_{sk, m} < 0 \end{matrix}$

$\begin{matrix} Δ T_{sk, m} = (T_{mean skin} - 34, 4) & [K] \end{matrix}$

$\begin{matrix} φ = 7, 94 * exp (- 0, 902 / (Δ T_{hy} + 0, 4) + \end{matrix}$ $\begin{matrix} 7, 612 / (Δ T_{sk, m} - 4)) [-]; φ = 0 when Δ T_{hy} \\ + 0, 4 \leq 0 or Δ T_{sk, m} - 4 \geq 0 \end{matrix}$

$\begin{matrix} Δ T_{hy} = (T_{hypothalamic} - 37, 0) & [K] \end{matrix}$

$\begin{matrix} ψ = (τ_{-} + τ_{-}) / (1 + φ) & [-] \end{matrix}$

$\begin{matrix} τ_{-} = 0, 11 * {dT}_{sk, m} / dt & [-] & ; for {dT}_{sk, m} / dt < 0 \end{matrix}$

$\begin{matrix} τ_{+} = 1, 91 * ({dT}_{sk, m} / dt)_{max} . exp (- 0, 681 * Δ t) \\ [-]; for {dT}_{sk, m} / dt > 0 \end{matrix}$

$\begin{matrix} Δ t = t - t_{0} & [h] \end{matrix}$

$\begin{matrix} t_{0} = time of occurrence of highest rate \\ {dT}_{sk, m} / dt [h] \end{matrix}$

5 Predicted percentage of dissatisfied

The individual assessments result in a certain spread around the average value. It is therefore useful to predict the percentage of people who normally experience the thermal environment as uncomfortable (PPD). This PPD (Predicted Percentage of Dissatisfied) can be derived from the PMV (Predicted Mean Vote), according to (NEN-EN-) ISO-7730 [11]. The PPD provides a quantitative prediction in percentage terms of the number of people who are dissatisfied with the thermal climate. DTS and the PMV are in general agreement with each other [9] and it is possible to calculate the PPD using the following formulation:

PPD = 100-95*(–0.03353*DTS^∧4-0,2179*DTS^∧2) [% ].

6 Validation and modification of the Stolwijk model

The characteristics of the multi-segmented human thermal model of Stolwijk were evaluated by Munir et al. [7] using skin temperature measurements at low activity in transient environments by comparing the results of two series of experiments, involving ten and seven subjects. The subjects were exposed to stepwise changes in environmental conditions, including neutral, low, and high ambient temperatures. It was concluded that the original Stolwijk model accurately predicted the absolute value and the tendency of the transient mean skin temperature. This suggests that the original Stolwijk model was valid for the prediction of the transient mean skin temperature of an “average” person in low-activity conditions. Some of the body segments showed deviations of local skin temperature. Modification of the distribution of the basal skin blood flow and the distributions of vasoconstriction and workload significantly improved the predicted results of both thermal neutral condition and thermal-transient conditions [7].

The above mentioned modifications are displayed in Table 1 and included in this modified Stolwijk model.

7 Steady state

Along with the development of a thermo physiological model, based on Chinese people (SJTU model). Zhou et al. compared a number of models for a stationary situation. Table 2 shows the prediction results of Zhou et al. [13] with different thermal sensation models, all based on western people. For comparison, the calculation results of the modified Stolwijk model are included at the end of Table 2.

The Stolwijk model in combination with the DTS2 version of the dynamic thermal sensation, in the stationary situation, best approximates the Fanger/ISO 7730 model.

8 Step changes in ambient temperature

In the experiments of Gagge et al. [14] three semi-nude (dressed only in shorts) male subjects, seated quietly, were exposed for two hours of steady state ambient temperatures of around 13, 18 and 48°C. The two-hour exposures to around 18°C and 48°C were part of two separate four-hour experiments in which the subjects underwent sudden changes in ambient temperature from neutral thermal sensation to the particular climate and back to neutral. The subjects were quickly transferred after one hour (t = 60 min) into another room at either 18°C or 48°C. After 2 hours (t = 180 min) the subjects moved back into the neutral environment for one hour. The wall temperature was equal to the temperature of the still air. Air movement was constant at 0, 05 m/s and the relative humidity was less than 40%.

The results of the experiments as well as the results of the simulation with the modified Stolwijk model are displayed in Figs. 3 to 6.

The Shitzer et al. [15] research ran three experiments with five young male subjects (age 22–27 years) to investigate the effects of three different environments on the recovery from heat stress. The duration of all three experiments was two hours. The first hour was spent on a bicycle ergometer working at a load of about 60 Watt in a 40°C and about 25% relative humidity chamber. In the second hour, subjects were exposed while sitting in a more comfortable environment. These environments included a fixed temperature equal to the one preferred by each subject in a preliminary test (condition 1) and two varied schemes which were either at 5°C above (condition 2) or 5°C below (condition 3) the preferred temperature. Changes in chamber temperature were made according to the subjects requests.

9 Temperature ramp

The study of Berglund and Gonzalez [16] consisted of testing subjects dressed in three different levels of clothing (0, 38, 0, 54 and 0, 74 clo_intrinsic) each of whom experienced seven rates of temperature change (0,±0, 5,±1 and±1, 5 K/h). Twelve college age subjects (6 men and 6 women) were exposed for each of the 21 test conditions. The 0 K/h tests were used as controls. The air and wall temperatures were always equal and the air movement was constant 0,1 m/s. Throughout the testing the dew point was 12 °C. Each subject was randomly assigned to a group of three men and three women. There were six groups in all for a total of 36 participants. Each group tested seven random combinations of clothing and temperature change including a control condition on seven consecutive afternoons. Two different groups experienced each test condition.

The subjects entered the test chamber at 12 : 30 p.m. Until 1 : 00 p.m. the temperature was held at a constant 25°C at which time the temperature ramp commenced. Every half an hour starting at 1 : 00 p.m the subjects marked a thermal response ballot to indicate their judgment of thermal sensation, discomfort and thermal acceptability. The subjects were not allowed to discuss the environment or how they felt. The subjects were not given any information about the environment or that it was changing. During the tests the subjects did other things i.e. conversed, studied, played games or did sewing and sketching. They were not completely sedentary but walked slowly around the test chamber for five minutes every thirty minutes (≈ 1, 2 met) [16].

According to Berglund and Gonzalez [16] the mean thermal sensation votes of the experiments were described by a multiple linear regression in terms of the operative temperature and clo_nevin:

Tsens = 0,305*T_operative+0,996*clo_nevin–8,08 (r = 0,95).

Herein is:

Tsens = thermal sensation, according to a seven point scale [–]

T_operative = The operative temperature [°C]

Clo_nevin = the clothing resistance according to the method used by Nevin [clo]

Clo_intrinsic = 0,79*Clo_nevin [17].

The simulated situations with the Stolwijk model are plotted against thermal sensations for all test conditions [16] in Figs. 9 to 26.

10 Cyclic variations in operative temperature

Schellen [18] studied the effects of moderate temperature drift on physiological responses, thermal comfort, and productivity of eight young adults (age 22–25 years) and eight older subjects (age 67–73 years). The subjects were exposed to two different conditions: S1-a control condition; constant temperature of 21.5°C; duration: 8 h; and S2-a transient condition; temperature range: 17–25°C, duration: 8 h, temperature drift: first 4 h:+2 K/h, last 4 h:–2 K/h. The subjects visited the climate room on two occasions (S1 and S2) with different indoor climate conditions. The order of the conditions alternated (e.g. subject 1 started with S1 and ended with S2, subject 2 started with S2 and ended with S1, subject three started with S1, etc.). To increase the mixing of the air, a fan was installed, resulting in air velocity near the subject of 0,19 m/s. The total heat resistance of the clothing, including desk chair, was approximately 0.98 clo. The subjects continuously performed office tasks; their metabolic rate was approximately 1.2 met [18].

The simulated S2-situation with the Stolwijk model was plotted against thermal sensations for all test conditions [18] in Fig. 27.

In the study of Nevin et al. [19] a total of eleven female office workers and seven male college students participated in the experiments. The individuals were combined in three groups; each group participated on separate days. The groups were classified into five young females (22 years±3 years standard deviation), six older females (44 years±11 years standard deviation) and seven males (25 years±4 years standard deviation). Because at the time of the experiment only four elderly females were available along with two 33-year-old it was decided to include all six as a separate group referred to only as “older female group”. Elderly males were not available at the time of the experiments. All subjects were in good health and were paid for their participation. Each group was exposed simultaneously to a air temperature swing of±0,3 K/min (Tair_mean = 25°C, Tair_max = 30°C, Tair_min = 20°C) during two hours. Each of the subjects rested on a plastic/aluminium legged office chair for 15 minutes and walked around the chamber at a rate of 50 steps/min for 5 minutes. The pace was kept constant by using a metronome. The activity level for the walking period for both male and female subjects was about 1,2 met. for a total of 15 minutes, with a rest of 5 minutes. The mean air velocity was 0,1 m/s and relative humidity was kept constant at 50%. During the first half hour the air temperature was set at 25°C [19].

The simulated situation with the Stolwijk model was plotted against thermal sensations for the test conditions with the older females and the younger males and females respectively in Figs. 28 and 29.

11 Conclusion

It was concluded on the basis of the calculations and the experimental results that:

In general the second version of the dynamic thermal sensation (DTS2), combined with the Stolwijk model, proved to be more accurate than the first version (DTS1).

Especially in a quiet constant linear temperature decreasing situation, at the cold end of the comfort zone, the experimental results better match with the thermal sensation, according to the first version of the dynamic thermal sensation model of Fiala (DTS1), in combination with the Stolwijk model.

The Stolwijk model is more valuable by improving the simulation of the skin temperature per body segment and by adding clothing and thermal sensation, suitable for the assessment of steady state and transient thermal conditions, and fixed with this the predicted percentage of dissatisfied. Based on the research of Munir et al. [7], an investigation on the improvement of the calculation of the skin temperature, the extent to which the Stolwijk model is suitable for the evaluation of local discomfort should be investigated. The Stolwijk model can, for example, be used for the assessment of individual ventilation and air conditioning systems. It is also possible to modify the Stolwijk model with individual characteristics, so the differences between subpopulations (e.g. young and old) can be assessed.

Conflict of interest

The author has no conflict of interest to report.

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