Influence of Thermal Shrinkage on Protective Clothing Performance during Fire Exposure : Numerical Investigation

The thermal shrinkage of protective clothing during fire exposure plays a crucial rule in reducing the clothing protective performance. The transversal reduction in the fabric perimeter around the body due to the fabric thermal shrinkage causes a dynamic reduction in the air gap between the clothing and the body. This leads to a dynamic change in the heat transfer modes within the gap. Despite of its influential effect on the clothing performance, the thermal shrinkage of protective clothing during fire exposure has not been yet addressed in the literature. This can be attributed to the absence of a gap model that can capture the reciprocal change in heat transfer modes within the gap due to clothing shrinkage. This paper develops a finite volume model to investigate the influence of the fabric thermal shrinkage on protective clothing performance. A special attention was drawn to the model of the air gap between the clothing and skin as it responds directly to the clothing thermal shrinkage. The influence of a variation in the fabric shrinkage rate and the overall reduction in the fabric dimensions was investigated. The paper demonstrates that the clothing protective performance continuously decreases with the reduction in the fabric dimensions while the decay in the clothing protective performance is limited to small shrinkage rates of the fabric. Moreover, this decay in the clothing performance vanishes at high shrinkage rates of the fabric.


Introduction
Protective clothing is widely used in many industries and applications such as petroleum and petrochemical industries and municipal firefighting to seek protection from thermal and fire exposures.The thermal protective performance (TPP) of the clothing is determined by estimating heat transfer from the thermal source to the skin through clothing, which causes skin burns as a result.Standard bench top tests (ISO 9151, 1995, ASTM D 4108, 1987, ASTM F, 1999, and NFPA, 2007) are used to evaluate the TPP of fabric specimens while manikin test (ASTM F, 2000) is used to evaluate the TPP of the whole garment at different locations of the body.
Modeling the thermal performance of protective clothing has been extensively reported in the literature during the past decade.Torvi (1997) and Torvi and Dale (1999) modeled heat transfer in Kevlar ® /PBI and Nomex ® flame-resistant fabric during a flame TPP test.Mell and Lawson (2000) modeled heat transfer in multiple layers protective garment during radiant exposure.Tan, Crown and Capjack (1998) studied the design of flightsuit protective garment for optimum protection to flight personnel.Chitrphiromsri and Kuznetsov (2005) and Song, Chitrphiromsri and Ding (2008) modeled heat and moisture transfer through firefighters' clothing in fire exposure and local flame test, respectively.Zhu and Zhang (2009) considered the fabric thermal degradation at high temperature during radiant exposure.Mercer andSidhu (2008, 2009) investigated the performance of protective clothing with embedded phase change material.
The air gap between the fabric and skin plays an essential role in determining the performance of protective clothing during fire exposure.This role was acknowledged in the literature in several studies.For example, Torvi, Dale and Faulkner (1999) investigated the effect of the gap width on the protective performance of a flame-resistant fabric during a flame TPP test.Sawcyn and Torvi (2005) and Talukdar, Torvi, Simonson and Sawcyn (2010) attempted to improve the modeling of the air gap in bench top tests of protective fabrics.The 3-D body scanning technology was used (Song, Barker, Hamouda, Kuznetsov, Chitrphiromsri, & Grimes, 2004;Kim, Lee, Li, Corner, & Paquette, 2002;Mah & Song, 2010a;Mah & Song, 2010b) to determine the widths and distribution of air gaps between flame-resistant garment and manikin body.Ghazy and Bergstrom (2010) developed a numerical model for single layer protective clothing that considers the combined conduction-radiation heat transfer between the fabric and the skin.Then, Ghazy and Bergstrom (2011) further investigated the influence of the conduction-radiation in the gap between protective clothing and the skin on the overall performance of the clothing.Ghazy and Bergstrom (2012) also developed a model for heat transfer in multiple layers firefighters' clothing that considers the combined conduction-radiation heat transfer within the air gaps between clothing layers.Ghazy (2013) developed a novel air gap model that stands middle way between the conduction-radiation model introduced in Ghazy (2011) and the approximate air gap model exists elsewhere in the literature.
The thermal shrinkage of protective clothing in thermal or fire exposures significantly affects the clothing performance.The transversal reduction in the fabric perimeter around the body due to fabric thermal shrinkage causes a dynamic reduction in the air gap between the clothing and the body.This leads to a corresponding variation in the total heat transfer through the gap and an interchanging variation in its modes.In addition, the reduction in the gap width caused by thermal shrinkage and hence the overall protective performance of the clothing depends on the total reduction in fabric dimensions and the shrinkage rate of the fabric.
The influence of the thermal shrinkage on the performance of protective clothing during fire exposure has not been yet addressed in the literature.This is because the lack of knowledge about shrinkage rates of fire-resistant fabrics during fire exposure.In addition, the approximate analysis of the air gap that most of the models in the literature adopted is not capable of considering the dynamic variation in the air gap between the clothing and the skin due to fabric thermal shrinkage.This paper numerically investigates the effect of the fabric's thermal shrinkage during fire exposure on the overall performance of protective clothing.A special attention was drawn to modeling heat transfer through the gap since it responds directly to the fabric thermal shrinkage.The temperature dependence of the thermophysical properties of the air gap and the fabric was accounted for.The influence of a variation in the fabric shrinkage rate and the reduction in the fabric dimensions on the clothing protective performance was studied to capture different forms of fabric thermal shrinkage.

Problem Description
A typical protective clothing system is shown in Figure 1.The clothing system comprises a fire-resistant fabric that is exposed to a heat flux of about 80 kW/m 2 from a lab burner, the human skin that consists of epidermis, dermis and subcutaneous layers and an air gap enclosed between the fabric and the skin.The energy equations for the clothing elements are expressed as follows.
Figure 1.A schematic diagram of protective clothing

Heat Transfer in Fire-Resistant Fabrics
The transient energy equation for the Kevlar ® /PBI fabric was introduced by Torvi (1997) and Torvi and Threlfall (2006) as where ρ is the fabric density, A C is the apparent heat capacity of the fabric, k is the fabric thermal conductivity, σ is Stefan-Boltzmann constant, g T is hot gases temperature, g ε is hot gases emissivity, γ is the extinction coefficient of the fabric and exp t is the exposure duration.
The boundary conditions of the fabric are is the emitted radiation from the fabric backside surface, which is discussed in section 2.2.The initial condition of the fabric is

Heat Transfer in the Air Gap
The transient heat transfer in the gap is written as where ρ , P c , and k are the density, specific heat, and thermal conductivity of the air gap, respectively and is the divergence of the radiative heat flux through the air gap.Note that for gap widths of 1/4 in.(6.4 mm) or less, the computed Rayleigh number within the gap is less than the critical Rayleigh number for nature convection heat transfer.That makes radiation and conduction are the dominant modes of heat transfer within the gap.
The width of the gap between the fabric and the skin due to fabric shrinkage is where y is the air gap width at any time t , o y is the nominal air gap width, y Δ is the reduction in the gap width due to the fabric thermal shrinkage and shk t is the time over which the fabric thermal shrinkage takes place, as shown in Figure 1.The Radiative Transfer Equation (RTE) of the air gap (Modest, 2003) is written as where I is the radiation intensity, s is the geometric distance, r v is the spatial position, s ˆis the angular direction and κ is the gap absorption coefficient.The unit direction s ˆ is defined in y-direction as where θ is polar angle, φ is azimuthal angle and y e ˆ is unit vector in y-direction.The black body intensity, b I , is defined as where T is the medium absolute temperature and σ is the Stephan-Boltzmann constant.
The boundary conditions for the RTE of the air gap (Equation 8) are written as  5) is calculated as ( ) where the incident radiation, ) (r G r , is defined as The radiation heat flux emitted from the fabric and that is incident on the skin surface are calculated as The RTE (Equation 8) is solved along with its boundary conditions using the Finite Volume Method (Chai & Patankar, 2000) where the facial intensity was related to the nodal one as follows.The boundary conditions for the air gap energy equation (Equation 5) are as follows.The initial condition of the air gap is

Heat Transfer in the Human Skin
Heat transfer in the human skin is modeled by the bioheat transfer equation developed by Pennes (1948).The energy equations for the epidermis, dermis and subcutaneous layers of the skin are written as where b ω is the blood perfusion rate, is the incident radiation heat flux on the skin (Equation 16) and ep L , ds L and sc L are the thicknesses of the epidermis, dermis, and subcutaneous layers, respectively.The initial conditions of the skin are represented by a linear temperature distribution from the epidermis surface (32.5ºC) to the subcutaneous base (37ºC).Skin burn injury takes place when the basal layer (the base of the epidermis layer) temperature reaches 44 o C. Henriques' integral (Henriques & Moritz, 1947) is employed to predict times for the skin to receive burn injuries as follows.
where the values for the activation energy E Δ of the skin and the pre-exponential factor P were determined by Weaver and Stoll (1996) for second-degree burns and by Takata, Rouse and Stanley (1973) for third-degree burns.The basal layer temperature is employed in the aforementioned integral to predict times to first-and seconddegree burns.First-and second-degree burns take place when ϕ reaches 0.53 and 1, respectively.Whilst the dermal base (the base of the dermis layer) temperature is employed in the integral to estimate times to third-degree burns, which occur when ϕ reaches 1.

Numerical Solution
The fabric, air gap and the skin (epidermis, dermis, and subcutaneous) energy equations were solved along with their boundary conditions using the finite volume method (Patankar, 1980) using the Gauss-Seidel point-by-point iterative scheme.The solution proceeds as follows.Within each time step, temperatures calculated in the previous time step are used as initial guess for the iteration loop.The air gap width is updated according to Equations 6 and 7. A uniform reduction in the air gap control volumes sizes is assumed whereas the air properties in each control volume do not change.Within the iteration loop, temperatures of the air gap, fabric backside and epidermis surface where fl h is the flame convection heat transfer coefficient, cnv h is the convection heat transfer coefficient from the clothing to the ambient surroundings, and reflectivity of the fabric backside, ep ε and ep ρ are the emissivity and reflectivity of the epidermis surface, s′ ˆ is reflected ray unit direction, n ˆ is unit normal to the surface and Ω′ d is solid angle containing the reflected ray.The divergence of radiative heat flux in the air gap energy equation (Equation epidermis surface temperature and air L is the air gap width.
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