The Deposition Of Radon Daughters And Daughter-Laden Aerosol On Rough Wall Surfaces

INTRODUCTION In order to understand the transport and deposition of radon daughters in mine atmospheres, it is necessary to know the variation in the attachment of the daughter atoms to particles as a function of particle size, composition, number density, relative humidity, temperature, and radon concentration, the free gaseous diffusion coefficients of the daughters, and the variation in the mass transfer of the activity, both free and attached to particles, to mine surfaces as a function of particle size distribution, surface roughness of the mine walls, and the flow conditions. If all of these parameters are known in a model system, it should be possible to understand the transport and fate of the airborne radioactivity in real mines under certain well-defined flow conditions. There have been a number of recent investigations of the attachment of radon decay products to particles 1-4, but there are still a number of unanswered questions regarding the process. However, it is clear that for most real mine atmospheres, the vast majority of the activity is attached to particles. The size distributions for the activity-bearing airborne particles have been studied 5,6, and it has been found that most of the activity resides on particles with diameters in the range of 0.05 µm to 0.3 µm with an average mass median diameter between 0.1 and 0.2 µm. The behavior of the unattached radon daughter species has also been recently studied[ 7], and many of the previous problems regarding the value of the diffusion coefficient for Po-218 have been resolved. A major problem in the understanding of the airborne transport of radioactivity in mines is the lack of detailed knowledge of mass tranfer to and fluid flow over rough walls under fully developed turbulent flow conditions. This paper will report the progress on a project that is designed to obtained that information. MATHEMATICAL MODEL DEVELOPMENT Deposition of particles on smooth surfaces in turbulent flow has been extensively studied. A comprehensive review of these results has been prepared by Sehmel 8. There has not been such a comprehensive study of particle deposition on rough walls under such flow conditions. In recent years, only a single model has been proposed to explain such deposition 9,10 and in both of these papers the flow structure in the rough walled pipe was not taken fully into account. As part of the work being conducted on this project, a more complete model was outlined in a previous report [11]. The basic theory will be reviewed to provide a context for the flow measurements to be reported. The flux of particle deposited on the walls of a pipe in a turbulent flow is derived from the one dimensional form of Fick's law as given by [N = Dpdpp/dr (1) where N is the flux of particles deposited per unit area per unit time, D is the total eddy diffusivity of the particles, p is the airborne concentration of particles, and pr is the distance measured from the center of the pipe. The rate of deposition is best expressed by a deposition velocity Vp = NIP pb (2) where P b is the mean particle concentration in the sulk flow. The shear radius, V/ut and the shear velocity, u , are used to calculate a nondimensional distance, and velocity, respectively, where v is the kinematic viscosity of the fluid. The nondimensional form of equation 1 is given by Vd = DP dpp(3) V dr+ where Pp = Pp/ Ppb(4) By integrating equation 3 from the rough wall stopping distance, S , to the center of the pipe, the deposition velocity can be obtained. In order to make this calculation, it is necessary to have accurate descriptions for the particle eddy diffusivity, stopping distance, and shear velocity in order to insure that the influence of the flow structure has been properly accounted for. The shear velocity can be determined experimentally from the shear stress evaluated at the wall, Tw, and the fluid density, ut =VT w/p = ub V f/2 (5) where ub is the mean bulk axial velocity. The wall shear stress for a given pressure drop, dP/dL, and hydraulic diameter, Dh, is]