2-D Modeling of a Walking Human-clothing System

MotivationWhen people are active, the air spacing between the fabric layer of a porous clothing system and the human skin changes with the activity level.

This change will cause air penetration in and out of the fabric and from openings. This air penetration will reduce the heat and moisture transfer resistance from the clothing.

Some of the previous models didn’t consider the effect of ventilation.

Others, developed empirical equations for ventilation that limited its use.

Those who developed theoretical models considered the air penetrating through the fabric to be in thermal equilibrium with the fabric, i.e same temperature and humidity ratio which is invalid

Objectives

In this work, a mathematical and numerical model is developed to study the effect of fabric motion (ventilation) fabric motion (ventilation) on the sensible and latent heat transporton the sensible and latent heat transport through the fiber clothing system with and without apertures.

The model is based on first principles of mass and first principles of mass and energyenergy conservation that made it flexible and widely used The model will help us understand how the moving human the moving human interacts with environmentally controlled placesinteracts with environmentally controlled places such as homes and offices, or in harmful environments with protective clothing such as fire fighting, or in work spaces. It also shows how the body behave thermally under different activity levels.

Research development• Normal Steady Ventilation of Clothing: Model & Find

Transport Coefficients• Normal Periodic Ventilation: Applicable to Clothed

Walking Human. (Closed Aperture Clothing)• Integrated Human Thermoregulatory Model and

Ventilation Model for a Walking Human• Incorporate Phase Change Material for the Clothing.

(Side Application Problem)• Extend the Model for 2-D Flow: ( Clothing with Open Apertures)- Combined Ventilation-Diffusion Model Applicable at

Low speeds of normal ventilation- Effect of Flow Modulation on air flow that enters from

the open boundary.

The flow in the axial direction is treated as fully axial direction is treated as fully developed laminar flowdeveloped laminar flow between two parallel surfaces with constant density and viscosity.

The flow at the opening is assumed to be ideal and is calculated by applying Bernoulli’s equation.

x

Pym aax

12

2

The axial mass flow rate per unit area can be written as:

Governing Equation

Modeling of the Air Mass Flow Rate

)2sin( ftyyy o

x

mym

t

y axay

a

)(

)(

PPP

mm

aay

i + 1, ji, ji - 1, j

mxi+1,j

myi,j

Fabric moving is up

Fabric is moving down

i + 1, ji, ji - 1, j

myi,j

mxi+1,jmxi,j

mxi,j

The fabric sinusoidal motion is represented by:

The general air layer mass balance is given by:

The mass flow in the normal direction is proportional to the pressure difference. It’s amount depends on the permeability of the fabric material. In this study the permeability of the fabric is considered constant. The airflow rate is then represented by:

Governing Equation

The flow in the axial direction is treated as fully axial direction is treated as fully developed laminar flowdeveloped laminar flow between two parallel surfaces with constant density and viscosity.

The flow at the opening is assumed to be ideal and is calculated by applying Bernoulli’s equation.

x

Pym aax

12

2

The axial mass flow rate per unit area can be written as:

Governing Equation

Water Vapor Mass balance:During the upward motion of the fabric, the air flow into the air spacing layer comes from the air void node of the fabric

During the downward motion of the fabric, the air flow will be out of the air spacing

2/

)()(

][)(

)(

f

avoidaaax

voidayaskairskinmaa

e

wwD

x

wmy

wmPPht

yw

2/

)()(

][)(

)(

f

avoidaaax

aaaskairskinmaa

e

wwD

x

wmy

wmPPht

yw

maywvoid

Fabricismovingupward

maxwa,i maxwa,i+1d(ρyWa)/dt

Hm(Psk-Pa)

Governing Equation

Energy balance of the air layerDuring upward motion:

][][)( )()(, askairskincaskfgairskinmtfgaava TThPPhht

yPhwTCy

t

x

hwTCmhwTCm fgaapaxfgvoidvoidpa

)]([][

2/

)(

2/

)(

f

avoida

f

avoidafg e

TTk

e

wwDh

During the Downward motion:

][][)( )(, askairskincaskfgairskinmtfgaava TThPPhht

yPhwTCy

t

x

hwTCmhwTCm fgaapaxfgaapa

)]([][

2/

)(

2/

)(

f

avoida

f

avoidafg e

TTk

e

wwDh

Governing Equation

The water vapor mass balance in the air void node is given by:

][][)( 'voidomovoidafvoidfa PPHwwmwe

t

2/

)(

2/

)(

f

voida

f

voidaa

e

wwD

e

wwD

Pa(x) < P

][][)( 'voidomovoidaafvoidfa PPHwwmwe

t

2/

)(

2/

)(

f

voida

f

voidaa

e

wwD

e

wwD

Pa(x) > P

Governing Equation

Results

0 10 20 30 40 50

x ( cm )

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

Am

plit

ude

of p

aral

lel

mas

s fl

ow r

ate

( kg

/s/m

)

The variation of axial flow rate as function of time and x.

0.00000

0.00004

0.00008

0.00012

0.00016

Am

plitu

de o

f no

rmal

mas

s fl

ow r

ate

( K

g/s/

m )

0 10 20 30 40 50

x ( cm )

The variation of normal flow rate as function of time and x.

The temperature variation in time of the internal air layer temperature at x=0, 0.5L, 0.8L and L.

x = 0. 8L

1-D

x = 0.8Lx = 0.5Lx = 0

x = L

990 992 994 996

Time ( sec )

998 1000298

300

302

304

306

308

Air

Lay

er T

empe

ratu

re (

o K )

310

The spatial variation in x-direction of the mean steady periodic temperatures of outer node and the internal air layer.

Plot Title

0 10 20 30 40

X ( cm )

50301

302

303

304

305

306

TE

MP

ER

AT

UR

E (o K

)

307

Fabric outer node temperature

Air layer temperature

Spatial average 2-D

1-D

990 992 994 996 998 1000

Time ( sec )

304.0

304.5

305.0

305.5

306.0

306.5

307.0

Air

Lay

er T

empe

ratu

re o K

The space-averaged temperature over the length of the domain L and the air layer temperature of the 1-D model.

Spatial average sensible heat loss

Spatial average latent heat loss

0

100

200

300

400

500

600

Ave

rage

Lat

ent a

nd S

ensi

ble

Hea

t Los

s (W

/m2 )

0 10 20 30 40 50

X ( cm )

The time-average variation in the sensible and latent heat losses from the skin in W/m2.

Model

f = 20 rpm f = 25 rpm f = 30 rpm

QL

(Watt/m2)

QS

(Watt/m2)

QL

(Watt/m2)

QS

(Watt/m2)

QL

(Watt/m2)

QS

(Watt/m2)

1-D Normal flow model(closed aperture)

198.2 37.31 233.7 43.86 265.27 49.71

2-D Flow Model (open aperture)

173.645 33.495 203 38.8 229.465 43.64

The time-space averaged sensible and latent heat losses at various ventilation frequencies, and the corresponding heat losses of the 1-D normal flow model.

The presence of the opening has resulted in lower sensible and latent heat loss than the 1-D model representing the closed aperture. These results are consistent with published experimental data of Loten and Danielsson (1993). Loten has reported experimentally that vapor resistance from the body at zero walking speed and 0.2 m/s wind is slightly higher for closed aperture than for open aperture.

Similar results have been reported by Danielsson on higher heat loss and higher internal convective coefficients for closed aperture clothing over various body parts as compared to respective values for open aperture clothing at walking conditions.