Improving local ventilation prediction by accounting for inter-segmental ventilation

Abstract

The inter-segmental ventilation rate at clothing inter-connection of arms and trunk affects the estimation of local ventilation rates of these clothed segments. The accurate estimation of the inter-segmental ventilation rate is based on the integration of a connected clothed cylinders model with a bio-heat model to predict a realistic segmental skin temperature. This integration is validated with experiments on a thermal manikin using the tracer gas method. The results show that accounting for the inter-segmental ventilation rate improves the estimation of the segmental ventilation of the arm and the trunk for different garment apertures at external wind velocities less than 4 m/s. For a wind velocity of 1 m/s, the inter-connection increased the trunk ventilation by up to 12% and heat loss by up to 5.46%.

A statistical correlation is established for the inter-segmental ventilation rate in terms of the influencing parameters: air permeability, wind velocity, mean air gap size between skin and clothing, and the upper clothing aperture design. Furthermore, a local ventilation rate correction factor equation is developed as a function of the inter-segmental ventilation rate to correct for local ventilation rates when derived from values of isolated/unconnected clothed segments.

Keywords

inter-segmental ventilation tracer gas clothed human heat losses segmental clothing ventilation

Over the years, researchers have been interested in measuring the clothing ventilation of the human body. The main reason is that clothing ventilation is an effective method for bringing thermal comfort and reducing heat strain in warm conditions. Historical prediction of overall clothing ventilation focused on the experimental approach. Two methods for the measurement of overall clothing ventilation have been developed; one by Crockford¹ and one by Lotens and Havenith.² Crockford’s method¹ is based on the measurement of the micro-environment volume. However, the Lotens and Havenith appoach² is based on a tracer gas method. A comparison between these two methods³ shows that both have acceptable reproducibility and sensitivity for a large range of ventilation values. Nevertheless, Crockford’s method¹ requires measurement of the clothing microclimate volume, which is known to be complicated and error susceptible.

Recently, more research has focused on local clothing ventilation because of its effect on evaluating segmental thermal comfort rather than overall thermal comfort.^4–8 Estimating local clothing ventilation has taken two tracks: empirical and analytical. The empirical approach is based on finding the steady clothing ventilation rate experimentally by using the tracer gas method.^6–8 However, in order to simplify the experimental approach, the estimated segmental ventilation approach either neglects the effect of air exchange between the connected clothing segments,^6,7 or uses sealed connections between the clothing segments to study the effect of other parameters on local ventilation.⁸ The analytical approach of clothed disconnected body segments is based on modeling the clothed segments as clothed heated cylinders and solving the coupled momentum, mass, and heat balances of the microclimate of air and clothing. These approaches treat the human body as independent clothed segments to predict the overall air mass flow rate entering through clothing and the heat lost from the body.^9–13 However, the analytical approach assumes artificial adiabatic closed inter-connection boundary condition for the clothed limb or trunk at the connection.

Ismail et al.¹⁴ were the first to recognize the influence of clothing inter-connection air exchanges between clothed segments on local and overall clothing ventilation rates. They developed a complex model for estimation of the inter-segmental ventilation rate, defined as the air exchanges between clothed arms and trunk. They found that the inter-segmental ventilation rate was substantial at relatively high wind speed and high clothing air permeability, and should not be neglected. Moreover, they reported that accounting for the inter-segmental ventilation rate resulted in more accurate predictions of overall clothing ventilation. Indeed, the relative error between the predicted and published experimental overall clothing ventilation data was reduced from 15% to 8% when incorporating the inter-segmental ventilation rate at relatively high wind speed and air permeability. However, the applicability of the Ismail et al.¹⁴ model is limited because it requires the segmental skin temperatures as inputs. Therefore, it is of interest to integrate the Ismail et al. model with a multi-segmental bio-heat model to obtain accurate segmental skin boundary conditions for a given metabolic rate. Although many bio-heat models exist in the literature, a multi-segment thermally responsive bio-heat model with low computational cost is selected to accurately predict segmental skin temperature and heat losses.^15,16

The validation of the integrated model requires development of an improved experimental approach that finds the local clothing ventilation rate and the inter-segmental ventilation rate. The improved approach is based on a modified experimental protocol for the tracer gas method to determine segmental and inter-segmental ventilation rate. Afterwards, an inter-segmental ventilation rate correlation is established as a function of the influencing parameters: air permeability, wind velocity, mean air gap size between skin and clothing, and the upper clothing aperture design. Because (1) the literature presented extensive data^4–8 on the estimation of the local ventilation rates without taking into account the inter-connection between human body segments, and (2) it is easier to experimentally measure the local ventilation while ignoring interconnection air exchanges, this study introduced a correction factor for these local ventilation rates. The relevance of this correction factor arises from the fact that estimating the local ventilation rates either analytically or experimentally requires more complexity when taking into account the inter-connection between clothed segments.

Therefore, the aims of this study are to (1) integrate the model of Ismail et al. with a bio-heat model; (2) validate the integration with a new experimental approach to account for the inter-connection between clothed segments; (3) find an inter-segmental ventilation rate correlation as a function of influencing physical parameters; and (4) adjust the available local ventilation rate data obtained using separate/unconnected clothed segments by a correction factor to account for the inter-segmental ventilation rate.

Research methods

In this study, the research approach follows the following strategy. First, the recently developed mixed convection connected clothed cylinders model of microclimate air of the human upper body of Ismail et al.¹⁴ is integrated with a segmental bio-heat model to ensure a realistic skin thermal boundary for the prediction of upper body inter-segmental ventilation rate. Second, a multi-stage experimental protocol is applied on a thermal manikin using a tracer gas method to estimate directly the inter-segmental ventilation rate and the local ventilation rates with and without clothing inter-connection between the clothed arm and trunk. Afterwards, the integrated bio-heat and ventilation model is validated with experimentally obtained values. This is followed by extensive simulations to develop, using SPSS statistical software, the desired correlations for the inter-segmental ventilation rate in terms of the influencing physical parameters, which include clothing properties, external wind velocity, and aperture design. Finally, the inter-segmental ventilation rate is used to establish a correction factor that adjusts the local ventilation rate, whenever it is estimated, for isolated/unconnected clothed segments and subject to external wind less than 4 m/s.¹⁴

Integration of the connected clothed cylinders model with a bio-heat model

A mixed convection connected clothed cylinders model of microclimate air of the human upper body was recently developed by Ismail et al.¹⁴ (see Appendix 2). Their model used six cylindrical segments: clothed cylindrical upper and lower arms, clothed trunk, and clothed shoulder connected to both trunk and arms. The connected clothed cylinders model needs the segmental skin temperatures as boundary conditions for the connected six cylindrical segments to predict the ventilation rate for each clothed cylinder and the inter-segmental ventilation rate through the path connecting the clothed arms to the clothed trunk. This model is improved in this current work by generating a realistic and accurate skin thermal boundary condition for each clothed cylindrical segment through coupling to a segmental multi-node responsive bio-heat model of the human body. The integration of the connected clothed cylindrical model to the bio-heat model not only produces more accurate inter-segmental and local ventilation rates of various segments, but also accurately predicts associated local heat losses.

The bio-heat model of Salloum et al.¹⁶ is coupled through the skin boundary condition (temperature) to the connected clothed cylinders model. Each segment (arms and trunk) has a different skin temperature.¹⁵ The fabric used in each segment is set in the bio-heat model, where the thermal properties of each fabric type play an important role in the heat transfer between the environment and the skin. The metabolic rate is set depending on the given activity level. The ambient conditions (temperature and humidity) and external wind velocity are also required as input to the bio-heat model. After setting all these parameters in the bio-heat model, the calculated skin temperature is then used in the mathematical model of the connected clothed cylinders. The resulting segmental ventilation rate is entered into the bio-heat model by means of the dynamic resistance for the ventilation through the fabric to predict the skin temperature.¹⁵ The new skin temperature is used again in the connected cylinder model to predict segmental ventilation. The alternating solution between the two models is repeated until convergence in skin temperature and segmental ventilation rate is obtained between the bio-heat model and the connected cylinders model. The convergence is attained after six iterations and takes about 35 minutes. A flow chart detailing the methodology for solving the integrated ventilation and bio-heat model is shown in Figure 1.
Figure 1.
Flow chart of the integration methodology.

Experimental methodology

The aim of the experiments is to determine the local ventilation of inter-connected segments in the upper part of the clothed human, as well as the air exchange rate that takes place at the inter-connection between the arm and trunk. Experiments are conducted on two types of jackets, one that is highly air permeable and one that is low air permeable.

For each clothing jacket case, three experiments are conducted on a thermal manikin for each of the two selected jackets using the tracer gas method, with three scenarios of tracer gas injection into: (1) the clothed trunk and the clothed arm simultaneously; (2) the clothed arm only; and (3) the clothed trunk only. In addition, a fourth experiment was conducted on the highly permeable jacket with closed connection between clothed arms and trunk while injecting the tracer gas in all segments. The purpose of the fourth experiment was to determine the difference in local ventilation when inter-connection was closed compared to values when inter-connection between the two segments was open.

Thermal manikin

The integrated ventilation model is validated experimentally using a 20-zone “Newton” thermal manikin¹⁷ (Measurement Technology Northwest, Seattle Washington, USA) as shown in Figure 2. The surface temperature or heating power of each body segment of the manikin can be controlled individually. All the thermal zones have embedded wire sensors to provide the required skin temperature or heat flux, with a standard deviation less than 0.01. The heat flux generated and associated surface temperatures are recorded during experiments at each body part by ThermDAC® software.
Figure 2.
Test setup of (a) the two large fans, (b) the manikin wearing the jacket, and (c) the locations and values of measured velocities in m/s in a virtual vertical plane (shown in white) at a distance of 0.35 m from the manikin front surface.

The system re-computes the set points and adjusts heating power every nine seconds. The cycle repeats until the convergence of the skin temperature or heat flux required based on the metabolic rate for a standing person.¹⁸ In the current study, the segmental skin temperatures are extracted from the validated bio-heat model¹⁶ and introduced to the software, as was also reported by Yang et al.¹⁹ The local heat fluxes generated during the experiment are recorded from the thermal manikin in order to approach the human body responses, so that the ventilation rates are measured at realistic segmental skin temperature.

Clothing ensembles

Two commercial jackets of the same medium size (Table 1), with high and low air permeability (Table 2), were selected for experimental testing. The air permeability of the fabric for each jacket were measured using an SDL MO2IA air permeability tester, with a standard deviation in repeated measurements of ±10⁻⁴ and accuracy of 0.1 L/(m²·s). Their thermal and evaporative resistances are measured using the sweating guarded hotplate (Model 306-200/400). The thermal insulation is also measured by the thermal manikin during the experiment. The lower part of the thermal manikin is dressed with the same clothing material with the same properties as the upper part. The lower part is closed at the waist level by a tight belt in order not to allow any air exchange between the lower part and the upper part. In addition, the gradient in temperature between the upper and lower parts at the waist level is relatively small, so that the conductive effect between these two parts can be neglected.
Table 1.
Basic dimensions (circumference) of the upper part of the thermal manikin and the medium size of the jacket

Bust (cm) Waist (cm) Hip (cm) Neck line (cm) Cuff (cm) Height (cm)

Thermal manikin size 93 74 93 35 11 65

Jacket size⁶ 120 110 116 38 14 65

Table 2.
Properties of the jackets used in the experiments

Physical parameters Jacket type

Sport jacket with high air permeability Jacket with low air permeability fabric

Material and composition 100% polyester High density polyethylene

Thickness (mm) 2.3 0.1

Weight (g/m²) 263 ± 1 75 ± 1

Fabric air permeability (m/s) 0.09 ± 10^–4 0.02 ± 10^–4

Thermal resistance (℃·m²/W) 0.056 ± 10^–5 0.018 ± 10^–5

Evaporative resistance (Pa·m²/W) 10.48 ± 0.05 22.57 ± 0.05

Thermal insulation (℃·m²/W) 0.105 ± 10^-5 0.06 ± 10^–5

External wind and climatic room conditions

Two large fans with a diameter of 0.5 m were installed vertically on a stand with controllable wheels to adjust the distance between the manikin and the stand for the desired velocity at the front side of the manikin. The stand center was placed on the horizontal line that passed through the upper body part center (trunk center) to provide symmetry of flow around it. The distribution of wind speed was measured by the manikin wind speed sensor, which was an air velocity transducer (model 8475-06) at 3-min intervals at twelve locations as shown in Figure 2(c) at a distance of 0.35 m from the manikin surface. The stand of the fan was moved away from the manikin so that the mean value of the twelve measured wind speed velocities was about 1.2 ± 0.015 m/s. Figure 2(c) shows that the wind speed distribution is uniform along the height and the width of the upper human part, with a maximum relative error of 7% between the maximum wind speed and the minimum wind speed.

The manikin and the fans are both placed in an environmental chamber. The chamber air temperature is measured by two manikin sensors at different heights (0.9 m and 1.6 m), and the average is about 24℃ ± 0.2℃. The relative humidity is measured at 1.6 m height and it is about 40% ± 3%.

Tracer gas method

The tracer gas method is applied only to the upper clothed part.⁸ Nitrogen was the selected tracer gas, since it is a safe, non-reactive, insensible gas, and it has the same properties as dry air. Since dry air is a mixture of nitrogen and oxygen and other components of relatively low percentage ( $C O 2 (%) = 100 (%) - C N 2 (%) - C other (%)$ ), any variation of the nitrogen concentration affects the oxygen concentration. Therefore, measuring oxygen concentrations allows us to calculate tracer gas concentration accurately.

Figure 3 shows the schematic diagram of our experimental setup that estimates the ventilation based on the tracer gas methods of Ke et al.⁸ for local clothing ventilation measurement. Two oxygen sensors of 2% accuracy and a standard deviation of ±0.01 are mounted in line at the inlet and outlet flow to and from the manikin microclimate air layer. A diaphragm pump (2–5 L/min) is used to circulate the extracted air from the manikin. The flow of air is controlled and measured by an air flow controller (0–5 L/min). Another flow controller (0–1 L/min) is mounted at the top of the nitrogen tank. The current experimental method/protocol to estimate local ventilation differs from that of Ke et al.⁸ in the following aspects:
nitrogen gas is used as tracer gas instead of argon;

the inter-connection openings in the upper human body part are left open;

with the added amount of nitrogen gas, the concentrations of oxygen gas are recorded at the inlet and outlet flow to and from the manikin microclimate.

Figure 3.
Schematic diagram of the experimental setup.
Taking advantage of symmetry, the distribution flow and the sampling flow are provided using tubes sealed to the right arm (or left) and half of the chest of the thermal manikin, perforated with holes of 1 mm diameter. The inlet flow and outlet flow are controlled to 1.6–2.3 L/min, while the added nitrogen flows are 0.2 L/min and 0.3 L/min. The values of flows are chosen depending on the jacket air permeability in order to be insignificant compared to the clothing ventilation.

The thermal manikin is turned on at a segmental skin temperature extracted from the validated bio-heat model, where the metabolic rate of 1.2 MET is given as an input. A MET is the ratio of the work metabolic rate to the resting metabolic rate at 58 W/m² × 1.8 m² of human skin area = 104 W. Once the heat fluxes generated during the experiments from each segments stabilize, the nitrogen tank is opened, and the flow controller mounted at the top of the tank is calibrated to the desired nitrogen flow. The diaphragm pump is switched on, and air extracted, depending on the flow rate specified by the air flow controller. The nitrogen is premixed with air in a small zone chamber before going into the clothing microclimate, so that the tracer gas injected at ambient conditions becomes instantaneously dispersed within the zone.¹⁸

The mixed air and nitrogen are injected at the front side and extracted at the microclimate conditions from the back side. The experiment is repeated until the steady-state conditions of the recorded inlet and outlet concentrations and the heat losses of the thermal manikin are reached. The circulated mass flow rate and the inlet and outlet concentration values are recorded. These values are used to solve the ventilation rate and inter-segmental ventilation rate equations. For the case of low air permeability fabric, the mass flow rate injected is controlled to be 1.6 L/min, including 0.2 L/min of nitrogen. For the case of high air permeability fabric (sport wear clothing), the mass flow rate injected is controlled to be 2.3 L/min including 0.3 L/min of nitrogen flow. The steady state is reached after 80 minutes for the high permeable fabric: 20 minutes for the model initialization and 60 minutes for the remaining part of the experimental procedure. In the case of low permeable fabric, the steady state is reached after about 100 minutes: 20 minutes for the model initialization and 80 minutes for the remaining experimental procedure for nitrogen injection. To ensure that results are independent of the injection and extraction locations of the inlet and outlet tubes, the experiment was repeated on the high air permeable jacket while placing two inlets and two outlets in the front and two inlets and two outlets at the back, and the concentrations were recorded after steady state conditions were reached in 80 minutes under the same nitrogen flow conditions. There was no significant difference between the recorded concentrations at steady state when the locations of the injection and extraction tubes were changed. The difference in concentration was less than 0.05%.

Calculations of local and overall ventilation with closed inter-connection

Mass balances of the tracer gas method, for determining overall and local ventilation through upper part of the human body were done by either neglecting the inter-segmental ventilation rate altogether^6,7 or by closing the connection between arms and trunk.⁸ In this protocol, simultaneous injection of nitrogen gas is performed into both the arm and trunk, and concentrations of oxygen are measured for inlet and out flows into the microclimate. The tracer gas mass balance for the microclimate ventilation for overall ventilation of upper body²⁰ or disconnected segment is given by
$\overset{\cdot}{q} in - out C in - \overset{\cdot}{q} in - out C out + \overset{\cdot}{q} vent C air - \overset{\cdot}{q} vent C out = 0$
(1)
where $\overset{\cdot}{q} in - out$ is the circulating mass flow rate (L/min), $C in$ and $C out$ are the oxygen concentrations of the garment inlet and outlet flow (%), $\overset{\cdot}{q} vent$ is the microclimate ventilation rate (L/min), and $C air$ is the oxygen concentration of the atmosphere. Then, the microclimate overall ventilation for negligible inter-segmental ventilation rate is calculated as
$\overset{\cdot}{q} vent = \frac{\overset{\cdot}{q} in - out (C in - C out)}{C out - C air}$
(2)

One experiment is performed on the high permeable fabric (α = 0.09 m/s) while the inter-connection between the arm and trunk is closed, and the experiment is repeated three times to ensure accurate results when inter-segmental ventilation is prevented. This provides a baseline measure for the significance of the inter-connection on local ventilation.

Measurement and calculation of inter-segmental and local ventilation rates

A modified experimental protocol for the tracer gas method is followed to determine segmental and inter-segmental ventilation rates. The method includes three experiments, and the calculation method adds new mass balances to replace equations (1) and (2), since we have three unknown parameters that require estimation. These three parameters are the microclimate ventilation of the trunk ( $\overset{\cdot}{q} vent - trunk$ ), the inter-segmental ventilation rate ( $IS$ ) due to connection, and the microclimate ventilation of the arm, ( $\overset{\cdot}{q} vent - arm$ ), as shown in Figure 4. In addition to the introduction of the inter-segmental ventilation rate as a new parameter, the direction of inter-segmental ventilation rate (from the trunk to arm or vice versa) is not known. The three experiments are as follows: (1) the first one follows the experimental protocol that includes simultaneous injection of nitrogen with the air flow entering the microclimate air of the arm and the trunk; (2) the second experiment involves injecting the excess nitrogen to the arm, and tracks its impact on the concentration of oxygen in the clothed trunk segment; and (3) the third experiment involves injecting the excess nitrogen into the trunk and tracking its impact on the concentration of oxygen in the clothed arm. Each experiment is applied to both ensembles, and is repeated at least three times to ensure that the test variability is lower than 5%.
Figure 4.
Schematic diagram of the three unknown parameters.

In the first experiment, the nitrogen is injected with the air flow entering both the arm and the trunk microclimate air layers. Since the inter-segmental ventilation rate should be accounted for in the calculations, the tracer gas equation (1) for the arm is modified to become
$\overset{\cdot}{q} in - out C in - arm + \overset{\cdot}{q} vent - arm C air + [max (IS, 0)] C out - trunk = [\overset{\cdot}{q} in - out + \overset{\cdot}{q} vent - arm . + max (IS, 0)] C out - arm$
(3)
where $\overset{\cdot}{q} in - out$ is the circulating mass flow rate (L/min), $\overset{\cdot}{q} vent - arm$ is the microclimate ventilation rate (L/min) of the arm, $IS$ is the inter-segmental ventilation rate (L/min) leaving the trunk to the arm, $C in - arm$ and $C out - arm$ are, respectively, the oxygen concentrations of the arm inlet and outlet flows (%), $C air$ is the oxygen concentration in the atmosphere (%), and $C out - trunk$ is the oxygen concentration of the trunk outlet flow (%). Similarly, the tracer gas equation for the trunk is given by
$\overset{\cdot}{q} in - out C in - trunk + 0.5 \overset{\cdot}{q} vent - trunk C air + [max (- IS, 0) .] C out - arm = [\overset{\cdot}{q} in - out + 0.5 \overset{\cdot}{q} vent - trunk + max (- IS, 0)] C out - trunk$
(4)
where $\overset{\cdot}{q} in - out$ is the circulating mass flow rate (L/min), $\overset{\cdot}{q} vent - trunk$ is the microclimate ventilation rate (L/min) of the trunk, $C in - trunk$ and $C out - trunk$ are, respectively, the oxygen concentrations of the trunk inlet and outlet flow (%), and $C out - arm$ is the oxygen concentration of the arm outlet flow (%).

Two additional equations are derived from single segment injection experiments three and four to solve for the three unknowns ( $\overset{\cdot}{q} vent - trunk$ , $IS$ , and $\overset{\cdot}{q} vent - arm$ ) and to determine IS direction from arm to trunk, or vice versa. Thus, one segment is injected with nitrogen while examining the concentration in the other non-injected segment. If the outlet concentration of the non-injected segment is below the atmospheric value, this means that a specific amount of air is being driven from the injected segment to the non-injected segment through the connection of the segments. Otherwise, the inter-segmental ventilation rate is either null or in the opposite direction. Equations are derived for the single segment injection experiment depending on the direction of the flow as follows
trunk tracer gas equation when excess nitrogen is injected in the arm microclimate (second experiment)

$0.5 \overset{\cdot}{q} vent - trunk C air + [max (- IS, 0)] C out - arm = [0.5 \overset{\cdot}{q} vent - trunk + max (- IS, 0)] C' out - trunk (if C' out - trunk < C air)$
(5{\rm a})

arm tracer gas equation when excess nitrogen is injected at the trunk microclimate (third experiment)

$\overset{\cdot}{q} vent - arm C air + [max (IS, 0)] C out - trunk = [\overset{\cdot}{q} vent - arm . + max (IS, 0)] C' out - arm (if C' out - arm < C air)$
(5{\rm b})
where $C' out - trunk$ is the oxygen concentration of the trunk in the outlet flow (%) after the injection of the arm, while $C' out - arm$ is the oxygen concentration of the arm in the outlet flow (%) after the injection of the trunk.

Solving equations (3), (4), and (5a) or (5b) determines segmental ventilation experimentally in the arm, trunk, and the inter-connection ventilation.

Results and discussions

Experimental evaluation and validation of IS and local ventilation rate using the integrated bio-heat and clothing inter-connected cylinders models

The analytical solution for the inter-segmental ventilation rate was obtained by integrating the mathematical model of the inter-connected clothed cylinders ventilation model developed by Ismail et al.¹⁴ with the segmental bio-heat model.¹⁶ The input parameters to the model used the values presented earlier in Tables 1 and 2 on the selected jackets’ dimensions and properties. It also used the environmental conditions in which the experiment was conducted at metabolic rate of 1.2 MET. The experimental calculations were obtained from the experiments done using the tracer gas method on a thermal manikin and from solving the mass balances of tracer gas for the three injection scenarios for the tracer gas, as described above.

For each clothing jacket case, three experiments were conducted, where nitrogen injection was (1) for both the clothed trunk and the arm; (2) for the clothed arm only; and (3) for the clothed trunk only. Table 3 presents the averaged recorded inlet and outlet concentrations for each tested jacket in each of the three experiments. It is evident that the outlet oxygen concentration for the trunk in both cases (low and high permeable fabric) was invariant and was similar to the ambient oxygen concentration when only the arm was injected with excess nitrogen. This means that, in both cases, the flow rate of microclimate air at the inter-connection was not driven from the arm to the trunk.
Table 3.
Recorded inlet and outlet concentrations

Injection scenarios Concentration (Case 1) Low air-permeable jacket Injection flow rate: 1.6 L/min
(Case 2) High air-permeable jacket Injection flow rate: 2.3 L/min

Recorded concentrations (%) with a standard deviation of ±0.01%

(i) N₂ injection is for both microclimates of arm and trunk C _in-trunk 18.4 18.3

C _in-arm 18.4 18.3

C _out-trunk 20.45 20.65

C _out-arm 20.45 20.55

(ii) N₂ injection is for the microclimate of the arm only C _in-arm 18.4 18.3

C’_out-trunk 21 21

(iii) N₂ injection is for the microclimate of the trunk only C _in-trunk 18.4 18.3

C’_out-arm 21 20.9

When the trunk was injected, different scenarios emerged for the two jackets. In the first case (low permeable jacket), the outlet oxygen concentration for the arm was similar to the ambient oxygen concentration when the trunk was injected with excess nitrogen. This means that negligible air mass flow rate was being driven through the connection from the trunk to the arm. Therefore, equations (3) and (4) need not be used and can be replaced by equations (1) and (2), neglecting the inter-segmental ventilation rate ( $IS$ ). On the other hand, the outlet oxygen concentration for the trunk in the second case of high permeable fabric was smaller than the ambient oxygen concentration, which means that a certain microclimate mass flow rate was being driven from the trunk to the arm, and should be computed. This emphasizes the effect of air permeability on the inter-segmental ventilation rate.¹⁴ In fact, the fabric air permeability allowed air to enter to the segmental microclimate air layers while the inter-connection allowed air exchange between the segments. Therefore in the case of high permeable clothing, equation 5(b) was used in combination with equations (3) and (4) to solve for the three unknowns: $\overset{\cdot}{q} vent - arm$ , $IS$ and $\overset{\cdot}{q} vent - trunk$ .

Figure 5 shows a comparison between the analytical and the experimental segmental ventilations for both cases. The error bars represent the range of the ventilation values found by the repeated experiments conducted for each case. Good agreement is observed between the analytical predictions of local and inter-segmental ventilations with those experimentally calculated. The relative error between the model and the experiment ranges from 5% to 10% for the high permeability fabric jacket, and from 6% to 14 % for the low permeability fabric jacket, with the highest error at low external wind. The results show that the inter-segmental ventilation rate was significant for the case when air permeability was relatively high. Indeed, the inter-segmental ventilation formed about 30% of the arm total ventilation and about 14% of the trunk total ventilation. Therefore, it is clear that inter-segmental ventilation rate should not be neglected, particularly when accurate estimation of segmental ventilation rate is sought.
Figure 5.
Comparison between the analytical and experimental ventilations in: (a) case 1 of low permeability clothing; (b) case 2 of high permeability clothing.

Table 4 presents a comparison between the analytical and experimental segmental ventilation and heat losses in both cases of open and closed connection for the high permeability fabric. The analytical heat losses are found from integrating the ventilation model with the bio-heat model. The experimental heat losses are given by the thermal manikin software and are defined as the necessary heat flux used to reach the segmental skin temperatures given from the bio-heat model at the given metabolic rate. Good agreement is observed between the analytical and the experimental results, with a relative error that did not exceed 10% for the segmental ventilation, and a relative error of a maximum of 5% for the segmental heat losses. Furthermore, the data presented in Table 4 reveal that inter-connection affects the segmental ventilation and heat losses for both arm and trunk. The heat losses and ventilation from the trunk decrease when the connection is closed. However, this decrease is compensated by an increase of the arm ventilation and heat losses. The main reason for this behavior is that the heated air that flows from the trunk to the arm when the connection is open allows more fresh air to enter the trunk. This fresh air increases the segmental ventilation of the trunk by 12% and the heat losses by 5.46%. On the other hand, the heated air that left the trunk and entered the arm decreases the arm ventilation by 3% and the heat losses by 6.68 %. The importance of this finding stems from the fact that the trunk is the most influential segment in body heat loss, and any increase in the trunk ventilation and heat losses will enhance thermal comfort.^21–24
Table 4.
Comparison between predicted and experimentally measured values of segmental ventilation and heat losses between open and closed connection

Segment Connection configuration Predicted value by model
Experimentally measured value

Ventilation (L/min) with a standard deviation of ±0.05

Arm open connection 11.26 10.56

closed connection 12.03 10.856

Trunk open connection 31.20 30.88

closed connection 28.63 27.5

Segment Connection configuration Heat losses (W/m²) with a standard deviation of ±0.05

Arm open connection 52.15 53.3

closed connection 56.70 57.12

Trunk open connection 64.91 65.4

closed connection 59.13 61.54

Correction of local ventilation for inter-connection air exchanges

The inter-segmental ventilation rate, IS, is defined as the air exchange between clothed arm and trunk induced by pressure differences at the connection between the two segments. The rate of these air exchanges is influenced by (12) external wind velocity (V_w), (2) clothing air permeability (α), (3) microclimate air gap size (Y), and (4) clothing apertures setting (open or closed at top or bottom ends of the clothed segments).¹⁴ Hence, a statistical correlation equation is sought for IS as a function of influencing parameters, as follows
$IS = φ (V w, α, Y)$
(6)

The statistical correlation sought is derived using the validated model results for the following three aperture cases for upper body clothing:
open clothed arm aperture at the bottom end and open clothed trunk aperture around the neck;

open clothed arm aperture and closed clothed trunk aperture;

closed clothed arm aperture and open top clothed trunk aperture at the neck.
Eighty simulations are performed using the developed mathematical model for each aperture design case to evaluate inter-segmental ventilation rate (IS) at equal increments of each of the influencing parameters at ambient conditions of 24℃ and relative humidity of 40%. The increment of air permeability is Δα = 0.01 m/s at constant V_w = 1.2 m/s and Y = 2.5 cm. The increment of wind velocity is ΔV_w = 0.1 m/s at constant α = 0.135 m/s and Y = 2.5 cm. The increment of air gap size is ΔY = 0.1 cm at constant α = 0.135 m/s and at constant V_w = 1.2 m/s.

The statistical analyses are performed using the SPSS© software package, where the predicted IS at each parameter are subject to a linear regression to derive a correlation for each aperture design. The SPSS software generates the correlations after a number of iterations, depending on the initial value given, until the relative reduction between successive residual sums of squares is of order of 10⁻⁸.

The generated IS statistical correlation equations as function of influencing parameters for clothing aperture cases A, B, and C are given by
$(A) IS = 83.68 \times α + 12.38 \times V w + 3.26 \times Y - 26.86 (R 2 = 0.982)$
(7{\rm a})

$(B) IS = 62.99 \times α + 9.61 \times V w + 2.27 \times Y - 19.86 (R 2 = 0.983)$
(7{\rm b})

$(C) IS = 84.08 \times α + 11.86 \times V w + 3.17 \times Y - 26.38 (R 2 = 0.981)$
(7{\rm c})
where α is the air permeability in m/s, V_w is the wind velocity in m/s, Y is the microclimate air gap in cm, IS is the inter-segmental ventilation rate in L/min. Figure 6 (a)–(c) shows the parity plot of inter-segmental ventilation rate for each clothing aperture case A, B, and C respectively. The observed values and the predicted values lie close to the $y = x$ line which indicated that the observed and the predicted values agree together. The applicability of the IS statistical correlations (7a), (7b), and (7c) is limited to the following rages of influencing parameters:
$airpermeabilityoffabric : 0.05 < α < 0.3 (m / s)$
(8{\rm a})

$windvelocity : 0.5 < V w < 4 (m / s)$
(8{\rm b})

$gapwidth : 0.5 \leq Y \leq 3 (cm)$
(8{\rm c})

Figure 6.
Inter-segmental ventilation rate (L/min) parity plot for case (a) open bottom and open top, (b) closed bottom and open top, and (c) open bottom and closed top.

The above ranges of permeability, wind speed, and air gap sizes constitute the limitation of our mathematical model. Note that when human body motion is present, the model is not applicable, since it changes the relative wind value and the gap width. It is of interest to note that the air gap size lay in the range used in the literature for non-moving human.^25,26 Indeed, Zhang et al.²⁵ used the range 0.5–1.9 cm, and Lu et al.²⁶ used the range 0.7–2.9 cm for microclimate air layer size. Moreover, the applicability of the IS correlations (equations (7a), (7b), and (7c)) can also be extended to other exposures in the range of 20–35℃ and a relative humidity of 40%–70%, since the variation of air temperature and relative humidity in these ranges does not significantly affect the ventilation rate or the inter-segmental ventilation.^11–13 The ambient thermal conditions affects only the natural convection induced in the air annulus. Studies by Othmani et al.¹¹ and Ghaddar et al.¹³ have shown that the natural convection effect on the local ventilation rate is less than 5%, and is only significant at low external winds and for low air permeability fabrics,¹¹ while relative humidity does not affect ventilation rates.¹³

A sensitivity analysis was performed to study the influence of each parameter on the inter-segmental ventilation rate. It is obvious that the inter-segmental ventilation rate increases with the increase of all three parameters, given that all the correlation coefficients multiplied by the air permeability, the wind velocity, and the microclimate air gap are positive. However, the rate of increase varied depending on the parameter. For example, an increase of 20% in wind speed resulted in about a 25% increase in the inter-segmental ventilation rate for the three aperture type cases. However, an increase of 20% in air permeability lead to an increase in IS of about 28 % for the same cases. The lowest rate of increase was observed for the air gap size, where a 25% increase in size lead to an increase of 18% only. This means that the air permeability is the most influencing parameter, followed by the wind speed and then the air gap size.

Local or segmental ventilation rates reported empirically in the literature use disconnected clothed cylindrical segment for the arm and the trunk, or neglected air exchange rates in the inter-connection between the clothed arm and trunk segments. The local ventilation rates of the clothed arm and trunk obtained from the literature for isolated segments are denoted by VR_arm and VR_trunk.

By following the same method adopted to find the inter-segmental ventilation rate statistical correlation, the correction factors of the arm and the trunk closed-connection ventilation rates are generated using a nonlinear regression method, as follows²⁷
$CF arm = \frac{CVR arm}{VR arm}$
(9{\rm a})

$CF trunk = \frac{CVR trunk}{VR trunk}$
(9{\rm b})
where CF_arm and CF_trunk are, respectively, the correction factors for the arm and the trunk local ventilation rates, and CVR_arm and CVR_trunk are, respectively, the realistic corrected ventilation rates of the arm and the trunk that account for the inter-segmental ventilation rate. Note that CVR_arm and CVR_trunk are obtained from clothed a connected cylinders model that calculates both local ventilation rates and intersegmental ventilation rates, and both parameters are influenced by IS. If IS is substantial, then the correction factor will deviate from unity.

As shown in equations (9a) and (9b), the correction factor is the ratio of the corrected local ventilation occurring when the inter-connection is open to the local ventilation occurring when the inter-connection is closed. The corrected local ventilation is predicted by simulating the validated integrated connected clothed cylinder model of the current work, while the local ventilation at zero IS is obtained using the unconnected clothed cylinder model.⁹ Therefore, the correction factors for local ventilations, VR_arm and VR_trunk, are given in equations (10a) and (10b), respectively, as follows
$CF arm = - 0.0014 IS 3 + 0.0127 IS 2 - 0.029 IS + 0.9719 (R 2 = 0.9855)$
(10{\rm a})

$CF trunk = - 0.001 IS 3 + 0.00837 IS 2 + 0.0134 IS + 1.0249 (R 2 = 0.9026)$
(10{\rm b})

The above correction factor correlations are applicable for the range of air permeability, velocity, and gap size given in equations (8a), (8b), and (8c), respectively. Since the clothing inter-connection causes a decrease of arm ventilation and an increase of trunk ventilation, CF_arm is always smaller than unity, while CF_trunk is always greater than unity. Using correction factors of equations (10a) and (10b) to adjust the experimentally estimated local ventilation of the arm and trunk when the inter-connection is closed for the high permeable fabric data (see Table 4), the resulting corrected local ventilation rates of the arm and trunk are equal to the experimentally obtained values when the inter-connection is open. Hence, additional confidence is provided in the obtained correlations using the unconnected clothed cylinder and the connected clothed cylinders models.

Conclusion

A methodology for predicting accurate and realistic local ventilation rates for clothed arms and trunk is developed. It is based on the integration of a connected clothed cylinders ventilation model with a segmental bio-heat model in order to predict inter-segmental and local ventilation rates. The validation of the integrated connected ventilation model is achieved by conducting an experimental approach on a thermal manikin using the tracer gas method. A modified experimental protocol for the tracer gas method is introduced to determine segmental and inter-segmental ventilation rates. The effect of inter-connection between clothed segments on the segmental ventilation and associated local heat losses are compared between the open and close connection apertures for a high permeability fabric. It is shown that the segmental ventilation of the trunk increases by 12%, and the heat losses by 5.46%, when the inter-connection is opened. Moreover, it is found that the heated air that leaves the trunk and enters the arm decreases the arm ventilation by 3%, and the heat losses by 6.68%, when the inter-connection is opened. A linear correlation is developed to estimate the inter-segmental ventilation rate as a function of air permeability, wind velocity, and air gap size. The correlation is used to find a correction factor for the local ventilation rates of the arm and the trunk when the inter-connection is not considered. This allows conducting an easier experiment and predicting more accurate ventilation rates.

	Bust (cm)	Waist (cm)	Hip (cm)	Neck line (cm)	Cuff (cm)	Height (cm)
Thermal manikin size	93	74	93	35	11	65
Jacket size⁶	120	110	116	38	14	65

Physical parameters	Jacket type
Material and composition	100% polyester	High density polyethylene
Thickness (mm)	2.3	0.1
Weight (g/m²)	263 ± 1	75 ± 1
Fabric air permeability (m/s)	0.09 ± 10^–4	0.02 ± 10^–4
Thermal resistance (℃·m²/W)	0.056 ± 10^–5	0.018 ± 10^–5
Evaporative resistance (Pa·m²/W)	10.48 ± 0.05	22.57 ± 0.05
Thermal insulation (℃·m²/W)	0.105 ± 10^-5	0.06 ± 10^–5

Injection scenarios	Concentration	(Case 1) Low air-permeable jacket Injection flow rate: 1.6 L/min	(Case 2) High air-permeable jacket Injection flow rate: 2.3 L/min
(i) N₂ injection is for both microclimates of arm and trunk	C _in-trunk	18.4	18.3
C _in-arm	18.4	18.3
C _out-trunk	20.45	20.65
C _out-arm	20.45	20.55
(ii) N₂ injection is for the microclimate of the arm only	C _in-arm	18.4	18.3
C’_out-trunk	21	21
(iii) N₂ injection is for the microclimate of the trunk only	C _in-trunk	18.4	18.3
C’_out-arm	21	20.9

Segment	Connection configuration	Predicted value by model	Experimentally measured value
Arm	open connection	11.26	10.56
closed connection	12.03	10.856
Trunk	open connection	31.20	30.88
closed connection	28.63	27.5
Segment	Connection configuration	Heat losses (W/m²) with a standard deviation of ±0.05
Arm	open connection	52.15	53.3
closed connection	56.70	57.12
Trunk	open connection	64.91	65.4
closed connection	59.13	61.54

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the financial support of the Lebanese National Council for Scientific Research (Grant number: 103061).

Appendix 1

Appendix 2

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Physical parameters	Jacket type
Physical parameters	Sport jacket with high air permeability	Jacket with low air permeability fabric
Material and composition	100% polyester	High density polyethylene
Thickness (mm)	2.3	0.1
Weight (g/m²)	263 ± 1	75 ± 1
Fabric air permeability (m/s)	0.09 ± 10^–4	0.02 ± 10^–4
Thermal resistance (℃·m²/W)	0.056 ± 10^–5	0.018 ± 10^–5
Evaporative resistance (Pa·m²/W)	10.48 ± 0.05	22.57 ± 0.05
Thermal insulation (℃·m²/W)	0.105 ± 10^-5	0.06 ± 10^–5

Injection scenarios	Concentration	(Case 1) Low air-permeable jacket Injection flow rate: 1.6 L/min	(Case 2) High air-permeable jacket Injection flow rate: 2.3 L/min
Injection scenarios	Concentration	Recorded concentrations (%) with a standard deviation of ±0.01%
(i) N₂ injection is for both microclimates of arm and trunk	C _in-trunk	18.4	18.3
	C _in-arm	18.4	18.3
	C _out-trunk	20.45	20.65
	C _out-arm	20.45	20.55
(ii) N₂ injection is for the microclimate of the arm only	C _in-arm	18.4	18.3
(ii) N₂ injection is for the microclimate of the arm only	C’_out-trunk	21	21
(iii) N₂ injection is for the microclimate of the trunk only	C _in-trunk	18.4	18.3
	C’_out-arm	21	20.9

Segment	Connection configuration	Predicted value by model	Experimentally measured value
Segment	Connection configuration	Ventilation (L/min) with a standard deviation of ±0.05
Arm	open connection	11.26	10.56
Arm	closed connection	12.03	10.856
Trunk	open connection	31.20	30.88
Trunk	closed connection	28.63	27.5
Segment	Connection configuration	Heat losses (W/m²) with a standard deviation of ±0.05
Arm	open connection	52.15	53.3
Arm	closed connection	56.70	57.12
Trunk	open connection	64.91	65.4
Trunk	closed connection	59.13	61.54