Ventilation rates of micro-climate air annulus of the clothing-skin system under periodic motion

A novel three-dimensional dynamic model is developed from first principles of mass and energy conservation of the modulated internal airflow in the variable annulus size between the clothing and the skin surface in presence of clothing apertures. The developed model solves for the flow and heat transfer problem in a finite length cylindrical annulus where the inner cylinder is oscillating within an outer fixed cylinder of porous fabric boundary. The changing annulus size induces pressure variations that cause air flow in the angular and the radial directions. In addition, axial airflow is present due to clothing open aperture to the atmosphere at one end of the annulus (sleeve or neck opening). The axial and angular flows in the trapped air layer are assumed locally governed by Womersley solution of time-periodic laminar flow in a plane channel in each direction. The 3-D model predicted the ventilation radial airflow through the fabric, the angular and axial airflow induced by the motion of the inner cylinder, and the sensible and latent heat losses from the skin due to ventilation with the presence of an open or closed aperture. Experiments were conducted using tracer gas method to measure time and space-averaged air ventilation rates induced by inner cylinder periodic motion within a fabric cylindrical sleeve at spacing amplitude ratio with respect to the mean of 0.8 for both closed and open aperture cases.The ventilation rates within the annulus predicted by the 3-D model agreed well with experimental data at higher frequencies. For closed aperture situation at an amplitude ratio of 0.8, the mean percentage errors of the measurements compared with the predicted values of the model were 52%, 27.5% and 6.7% corresponding to the frequencies of 30 rpm, 40 rpm, and 60 rpm, respectively. Measured ventilation rates for open aperture agreed well with predicted ventilation rates at high frequencies giving lower values of total air renewal than the closed aperture results where the measured reductions in total ventilation rate compared to closed aperture were 8.5% and 14.3% corresponding to the frequencies of 40 rpm and 60 rpm, respectively. In addition, the model results showed that under walking conditions, a permeable clothing system with an open aperture reduced the heat loss from the skin by less than 1% when compared to the closed aperture clothing system. These results are consistent with previously published empirical data on air layer resistance for open and closed aperture of high air permeable fabric.