In the majority of the past work on the problem of particle sampling it has been assumed that the particle Reynolds number associated with the motion of the particle relative to the fluid is sufficiently small for the Stokes drag to be applied. This is a reasonable assumption in many applications but as the particle Reynolds number increases the drag predicted by Stokes law deviates increasingly below the true value. The aim of this present work is to investigate the error incurred by neglecting the finiteness of the Reynolds number when considering the problem of particle sampling. As it is necessary to model the sampling procedure as accurately as possible it is important to know whether including realistic values of the Reynolds number in the model makes a significant difference to the results obtained. It was decided to adopt an analytical approach and not the B.I.E. method described in Chapter 4 as this is a first attempt at understanding the general effects of including the finite particle Reynolds number in the model on the sampling of the particles for any shaped sampler with a suction orifice. Therefore the cylindrical sampler shown in Fig.3.1 is investigated in detail. It is assumed that the particles are spherical and suspended in the fluid without sedimentation.

In Chapter 4 the case of blunt body sampling with two-dimensional samplers was considered using the B.I.E. method to evaluate the flow characteristics. In this Chapter the method is extended to model three-dimensional samplers. As an example a spherical sampler with a circular orifice on its surface with the flow approaching at an angle to the horizontal plane through the centre of the sampler, is considered. This is equivalent to considering the sampler orientated at an angle to the flow. It is found that the computation, and hence computing time, required is reduced when the flow is approaching the sampler parallel to its axis of revolution and hence the majority of results have been obtained for this situation.

In previous work, two different approaches have been adopted to modelling the problem of blunt body sampling, the combined theoretical and experimental approach adopted by Vincent and his co-workers and the analytical approach taken by Ingham. In this Chapter a comparison is made between the results obtained by Vincent and those obtained using an analytical approach.