Discrete Element Method (DEM) simulations are a promising approach to accurately predict agglomeration and deposition of micron-sized adhesive particles. However, the mechanistic models in DEM combined with high particle stiffness for most common materials require time step sizes in the order of nano seconds, which makes DEM simulations impractical for more complex applications. In this study, analytically derived guidelines on how to reduce computational time by using a reduced particle stiffness are given. The guidelines are validated by comparing simulations of particles with and without reduced particle stiffness to experimental data. Then two well-defined test cases are investigated to show the applicability of the guidelines. When introducing a reduced particle stiffness in DEM simulations by reducing the effective Young's modulus from E to E mod , the surface energy density γ in the adhesive Johnson-Kendall-Roberts (JKR) model by Johnson et al. [1] should be modified as γ mod = γ (E mod /E) 2/5. Using this relation, the stick/rebound threshold remains the same but the collision process takes place over a longer time period, which allows for a higher time step size. When rolling motion is important, the commonly used adhesive rolling resistance torque model proposed by Dominik and Tielens [2, 3], Krijt et al. [4] can be used by modifying the contact radius ratio (a/a 0) 3/2 to (a mod /a 0,mod) 3/2 , whilst keeping the other terms unaltered in the description of the rolling resistance torque M r,mod = −4F C (a/a 0) 3/2 ξ. Furthermore, as the particle stiffness is reduced from E to E mod , the time period for collisions (or oscillations when particles stick upon impact) ∆t col is found to vary as ∆t col,mod = ∆t col (E/E mod) 2/5. As the collision duration and the collision time step size are directly related, this criterion can be used to estimate how much the time step size can be changed as a reduced particle stiffness is introduced. Introducing particles with a reduced particle stiffness has some limitations when strong external forces are acting to break-up formed agglomerates or re-entrain particles deposited on a surface out into the free stream. Therefore, care should be taken in flows with high local shear to make sure that an external force, such as a fluid drag force, acting to separate agglomerated particles, is several orders of magnitude lower than the critical force required to separate particles.

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A numerical study has been carried out to investigate heat transfer enhancing flow field in 28 geometrically different sinusoidally, spirally corrugated tubes. To vary the corrugation, the height of corrugation e/D and the length between two successive corrugated sections p/D are varied in the ranges 0 to 0.16 and 0 to 2.0 respectively. The 3D Unsteady Reynolds-averaged Navier-Stokes (URANS) equations combined with the transition SST turbulence model are solved using the finite volume method to obtain the fully-developed flow field in a repeatable section of the heat exchangers at a constant wall temperature and at Re = 10, 000. By studying the wide range of geometrically different tubes, the flow conditions vary significantly. At low corrugation heights, only a weak secondary flow centred in the corrugated section is present. At higher corrugations heights, the tangential velocity component increases and eventually exceeds the axial velocity component causing the highest pressure to be located at the centre of the corrugated section. At these high corrugation heights, a further increase in corrugation height will at best only result in a small increase in Nusselt number but at a significantly higher pressure loss. To assess the performance as a heat exchanger, the ratio of enhanced Nusselt number to enhanced friction factor η = (Nu/Nu s)/(f /f s) 1/3 compared to the non-corrugated tube is used. Using this parameter, the simulations show a decrease in performance at higher corrugation heights. To link the detailed flow fields to the performance as a heat exchanger, non-dimensional correlations for heat transfer, pressure loss, and performance parameter are given.