The present research aims to to study the turbulence modulation in an particle-laden annular pipe flow, via Direct Numerical Simulation (DNS). The alteration of the heat exchange through the cylinder shells is also studied. The inter-phase momentum coupling is enforced with the recent Exact-Regularised Point-Particle method (ERPP). The research focuses on the particle agglomeration close to the wall, the so called turbophoresis. The correlation of this phenomenon to the friction wall drag and fluid thermal modification is explored. For this purpose the turbulent intensities, the fluid mean temperature and velocity profiles, the turbulent and viscous shear stresses and the mean particle concentration will be examined. The effect of wall curvature will be also explored. We plan to study different combinations of mass ratios and particle diameters, while the background turbulence is fixed. The Prandtl and the friction Reynolds numbers are Pr=0.7 and Re*=200, respectively. The particle to fluid density ratio is 180. The radial aspect ratio is Ri/Ro=0.25, where Ri and Ro are the internal and external wall radius, respectively. The equations to be solved are the incompressible Navier-Stokes equations, the Fourier equation and the particle momentum equation. The differential equations are implemented over a parallel code ( MPI ). The code will run in the clusters "Menrva", of the Department Aerospace and Mechanical Engineering ( DIMA ) of La Sapienza, and "Galileo" of the Cineca facility.
The research of multiphase dispersed flows has made much progress in the past decades. The one-way coupling regime has been widely explored and understood. However, the problems in modelling the singular feedback on a discrete ground has caused a setback in the last two decades. Two-way coupling effects can be important even for very dilute suspensions, and cannot be neglected. The simplest regularising procedure is undoubtedly Particle in Cell (PIC) [1]. However, the method provides several limitations and drawbacks [3]. In fact, the correct evaluation of the particle momentum equation calls for the computation of the undisturbed particle field [4]. This operation requires special numerical procedures in PIC [7]. Moreover, the method introduces numerical biases that can be mitigated only if the number of particles Np is higher than the computational points Nc, namely Np>Nc [3]. This limits the mass ratios that can be explored with PIC.
These problems are overcome at once with the introduction of the Exact Regularised Point-Particle method [8]. In fact, the only limit of the approach are the working hypothesis of dispersed multiphase flows: small void fractions and particle diameters (compared to l*). Moreover, in contrast to PIC, the method is convergent, meaning that decreasing the spacing only increases the resolution of the field. ERPP allowed for the first time to accurately explore, on numerical ground, turbulent dispersed flows in the two-way coupling regime. DNS of particle-laden shear flows have been studied, founding the potential of the discrete phase to alter the turbulence [9]. Similar results are obtained when the drag modification and the turbophoresis were investigated in a turbulent pipe flows [10].
The innovation of this research is the new configuration: the annular pipe. This is the first work that deals with such geometry, in the context of DNS. This will allow us to understand the role of the wall curvature on the multiphase system, a specific problem of non simply connected domains.
In our research the turbulence is seeded by thermally-neutral particles. This means that the particle feedback acts only on the momentum equations, leaving the Fourier equation uncoupled.
However, we plan to enforce the coupling also on the thermal field at a later step. This configuration provides a more realistic model. In fact, hot/cold particles represent a singular source/sink of heat for the fluid. The singular heat flux can be easily treated with ERPP, as for the momentum feedback.
The future perspectives of this research include to study the effects of the radial aspect ratio. The influence of this quantity in the single phase annular pipe is well-understood [11], but it is not clear which role could have in the particle turbophoresis or drag modification. Additionally, we intend to explore the effect of the Prandtl number on the inter-phase and wall heat exchange. Although there already exist works dealing with such effect in the single-phase flow [12], no one in the particle-laden context has been carried out.
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Volume 37, Issue 8,2010,Pages 958-963,ISSN 0735-1933