A particle being tracked in an LES flow field feels all the associated velocity fluctuations. In LESs (see, e.g., Crowe et al, 1996 Van den Akker, 2006), most of the turbulent motions of the flow field of the carrier phase are resolved. Hence, very realistic information on particle trajectories cannot be expected on the basis of RANS-based flow fields. Given the various and numerous assumptions of any turbulence model used for the RANS simulation and the degree of sophistication of the random walk model applied, a very accurate representation of the fluid–particle interaction force may not be very essential. Various particle dispersion models are available, such as discrete random walk models (among which the eddy lifetime or eddy interaction model) and continuous random walk models usually based on the Langevin equation (see, e.g., Decker and Sommerfeld, 2000 Dehbi, 2008). When nevertheless the turbulent motion of the particles is of interest, this can only be estimated by invoking a stochastic tracking method mimicking the instantaneous turbulent velocity fluctuations.
In RANS-based simulations, the focus is on the average fluid flow as the complete spectrum of turbulent eddies is modeled and remains unresolved. Now, only the aspects relevant for a proper application of the fluid–particle interaction force in these types of simulation will be highlighted. The difference between RANS and LES has been described elsewhere, e.g., Van den Akker (2006). In addition, we should distinguish between particle tracking in a flow field obtained by means of the very common RANS equations and particle tracking in a flow field simulated by the more advanced LES technique. The fluid–particle interaction can be treated in the simpler one-way mode or according to the more complicated two-way coupling mode in which the particles also affect the carrier phase flow field ( Decker and Sommerfeld, 2000 Derksen, 2003 Derksen et al, 2008).
Ignoring the mutual interaction of particles is therefore not too serious a simplification.
The use of the Euler–Lagrange approach, or point-particle method, is usually restricted to the more dilute gas–solid and liquid–solid systems. Although the flow around the particles is not resolved, any empirical correlation does reflect the hydrodynamics of the canonical case involved. The motion of the particle is simulated by means of Newton's second law and that is why the fluid–particle interaction force is needed and the empirical correlations enter. In the Euler–Lagrangian approach of two-phase flow (see, e.g., Crowe et al, 1996), the particles are treated as point particles: the finite volume of the particles is not considered and the flow around the particles is not resolved. While usually proper attention is being paid to the Reynolds number restrictions for the use of empirical correlations, these more generic considerations with respect to the details of the fluid mechanics hardly receive attention. The result of this drifting velocity is that the particles get dispersed. Obviously, inertial particles are not capable of exactly following the fluid velocity fluctuations (see also Dehbi, 2008) a drift correction velocity, or a drifting velocity, and an extra time scale pertinent to the turbulence as seen viewed by the particles may be used to take this effect into account ( Mudde and Simonin, 1999 Viollet and Simonin, 1994). Using the steady-state drag coefficient correlations for conditions in which a particle continuously experiences varying hydrodynamic conditions ignores the time scales needed for boundary layers and wakes to adapt to such variations. The common drag force correlations have been obtained under specific conditions: steady-state, no turbulence in the ambient stagnant fluid, no lift force (neither a result of shear flow in the fluid, nor due to particle rotation), and no adjacent particles or containment walls. Except for the Stokes regime of particle motions when the particle Reynolds number is smaller than 0.1 (or, less strictly, smaller than unity), simply adding in any type of CFD simulation a number of expressions derived for specific canonical cases to get the correct total interaction force conflicts with the nonlinear character of fluid flow and the Navier–Stokes equation. The above extensive explanation about fluid–particle interaction demonstrates how complex a topic this is when the approach is to draw up generally applicable empirical correlations with the view of using them in the common CFD simulations by means of the (commercial) CFD software. Van den Akker, in Advances in Chemical Engineering, 2015 10.1 The Euler–Lagrange Approach
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