The modelling of particle resuspension in a turbulent boundary layer

Abstract

The work presented concerns the way small particles attached to a surface are resuspended when exposed to a turbulent flow. Of particular concern to this work is the remobilization of radioactive particles as a consequence of potential nuclear accidents. In this particular case the focus is on small particles, < 5 microns in diameter, where the principal force holding such particles onto a surface arises from van der Waals inter-molecular forces. Given its suitable treatment of the microphysics of small particles, it was decided here to aim to develop improved versions of the Rock’n’Roll (R’n’R) model; the R’n’R model is based on a statistical approach to resuspension involving the rocking and rolling of a particle about surface asperities induced by the moments of the fluctuating drag forces acting on the particle close to the surface. Firstly, a force (moment) balance model has been modified by including the distribution of the aerodynamic force instead of considering only its mean value. It was also possible to improve the representation of the adhesive-force distribution where it is customary to include a substantial reduction factor to take account of surface roughness. The R’n’R model is significantly improved by using realistic statistical fluctuations of both the stream-wise fluid velocity and acceleration close to the wall obtained from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of turbulent channel flow; in the standard model a major assumption is that these obey a Gaussian distribution. The flow conditions are translated into the moments of the drag force acting on the particle attached to the surface (using O’Neill’s formula for the aerodynamic drag forces in terms of the local flow velocities). In so doing the influence of highly non-Gaussian forces (associated with the sweeping and ejection events in a turbulent boundary layer) on the resuspension rate has been examined along with the sensitivity of the fluctuation statistics to LES and DNS. We have found most importantly that the statistics of both fluctuating forces and its derivative (normalized on their rms values) are noticeably independent of the normalized distance from the wall, y+ within the viscous sublayer (y+ < 6) – if this were not the case then modelling fluctuations with different particle sizes would be far more complex. In particular as a result of the analysis of our DNS/LES data 3 distinct features of the modified R’n’R model have emerged as playing an important part in the resuspension. The first is the typical forcing frequency ω due to the turbulent (fluctuating) aerodynamic drag forces acting on the particle attached to a surface (in the modified R’n’R model based on the DNS results (y+ = 0.1) it is a factor of 4 > the value in the original model based on Hall’s measurements of the lift force). This naturally has a significant effect of increasing the fraction resuspended for very short times (ωt ~< 1) iv and is the controlling influence over the entire range of times from short to long term resuspension. The second is the value of the ratio of the root-mean-square (rms) drag force to its mean value which in the modified model is nearly twice (1.8) than that in the original. This feature of the model is largely responsible for the greater fraction resuspended after times ~ 1s (times which are sufficient to include the transition period from short term resuspension to long term resuspension rates (~t-1). The third feature introduces changes in the resuspension because the distribution of aerodynamic drag forces in the modified model is distinctly non-Gaussian behaving more like a Rayleigh distribution. This means that the distribution of the drag force decays much more slowly in the wings of the distribution than the equivalent Gaussian (with the same rms) so that for very large values of the adhesive force / rms drag force ~ 8 (at the extreme end of the DNS measurements), the resuspension rate constant is a factor of 30 larger than that for an equivalent Gaussian model. Thus although the fraction of particles resuspended is very small in these instances, the differences between the modified and original models can be very large. This is particularly important when we consider resuspension from multilayer deposits. When we consider these influences in the context of a broad range of adhesive forces due to surface roughness, we find that in general, the modified model gives around 10% more for the fraction of particle resuspension fraction than the original R’n’R model (for an initial log normal distribution of adhesive forces), however the difference could become significant (3 to 7 times greater depending on the range of values of the adhesive-force spread factor) when the friction velocity is small (i.e., smaller resuspension fraction). As for the short-term resuspension rate, the difference between the modified and original model becomes significant when this is dominated by the typical forcing frequency (ω+ is 0.0413 for the original model, 0.08553 for LES approach and 0.127143 for DNS for y+ = 6). The sensitivity to the adhesive-force spread factor has also been studied and the results indicate that the modified model removes particles much more easily than the original model in conditions of small friction velocity and a smoother surface (i.e., small spread factor). Finally in this phase of the work, the correlation between the distribution of the fluctuating force and its derivative has been checked for both LES and DNS statistics. The results demonstrate that this correlation has a very slight effect on particle resuspension compared with the result from the uncorrelated curve-fitted model. In view of recent numerical data for lift and drag forces in turbulent boundary layers (Lee & Balachandar), the lift and drag we have considered and the impact of these data on predictions made by the non-Gaussian R’n’R model are compared with those based on O’Neill formula. The results indicate that, in terms of the long-term resuspension fraction, the difference is minor. It is concluded that as the particle size decreases the L&B method will lead to less-and-less long-term resuspension. Finally the ultimate model that has been developed in this work is a hybrid version of the R’n’R model adapted for application to multilayer deposits based on the Friess and Yadigaroglu multilayer v approach. The deposit is modelled in several overlying layers where the coverage effect (masking) of the deposit layers has been studied; in the first instance a monodisperse deposit with a coverage ratio factor was modelled where this was subsequently replaced by the more general case of a polydisperse deposit with a particle size distribution. The results indicate that, in general, as the number of modelled layers increases the resuspension fraction of the whole deposit after a certain time decreases significantly. In other words, it takes a much longer time to resuspend a thicker deposit. Taking account of the particle size distribution slightly increases the short-term resuspension. However, this change decreases the long-term resuspension significantly. The model results have been compared with data from the STORM SR11 test (ISP-40) and the BISE experiments. In general, both comparisons indicate that with smaller spread of the adhesive force distribution (i.e., the range of adhesive force distribution is narrower) the new multilayer model agrees very well with the experimental data. It can be inferred that multilayer deposits lead to much narrower distributions of adhesive force.