Fully coupled simulations of monodisperse and bidisperse suspensions in a linear shear flow

The dynamics of macroscopically homogenous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of very small Reynolds and Stokes numbers using the Force Coupling Model (Lomholt & Maxey1). In this numerical approach, the velocity disturbance is obtained by a low order multipole expansion (particle forcing on the flow is represented by monopole and dipole terms spread on a finite volume envelop related to particle radius)

Connecting dispersion models and wall temperature prediction for laminar and turbulent flows in channels

In a former paper, Drouin et al. (2010) proposed a model for dispersion phenomena in heated channels that works for both laminar and turbulent regimes. This model, derived according to the double averaging procedure, leads to satisfactory predictions of mean temperature. In order to derive dispersion coefficients, the so called ‘‘closure problem’’ was solved, which gave us access to the temperature deviation at sub filter scale. We now propose to capitalize on this useful information in order to connect dispersion modeling to wall temperature prediction. As a first step, we use the temperature deviation modeling in order to connect wall to mean temperatures within the asymptotic limit of well established pipe flows. Since temperature in wall vicinity is mostly controlled by boundary conditions, it might evolve according to different time and length scales than averaged temperature. Hence, this asymptotic limit provides poor prediction of wall temperature when flow conditions encounter fast transients and stiff heat flux gradients. To overcome this limitation we derive a transport equation for temperature deviation. The resulting two-temperature model is then compared with fine scale simulations used as reference results. Wall temperature predictions are found to be in good agreement for various Prandtl and Reynolds numbers, from laminar to fully turbulent regimes and improvement with respect to classical models is noticeable

Development of filtered Euler–Euler two-phase model for circulating fluidised bed: High resolution simulation, formulation and a priori analyses

Euler–Euler two-phase model simulations are usually performed with mesh sizes larger than the smallscale structure size of gas–solid flows in industrial fluidised beds because of computational resource limitation. Thus, these simulations do not fully account for the particle segregation effect at the small scale and this causes poor prediction of bed hydrodynamics. An appropriate modelling approach accounting for the influence of unresolved structures needs to be proposed for practical simulations. For this purpose, computational grids are refined to a cell size of a few particle diameters to obtain mesh-independent results requiring up to 17 million cells in a 3D periodic circulating fluidised bed. These mesh-independent results are filtered by volume averaging and used to perform a priori analyses on the filtered phase balance equations. Results show that filtered momentum equations can be used for practical simulations but must take account of a drift velocity due to the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and particle sub-grid stresses due to the filtering of the non-linear convection term. This paper proposes models for sub-grid drift velocity and particle sub-grid stresses and assesses these models by a priori tests

A posteriori study of filtered Euler-Euler two-phase model using a high resolution simulation of a 3D periodic circulating fluidized bed

Gas-particle flows in vertical risers are involved in many industrial scale fluidized bed applications such as catalytic cracking, fossil or biomass combustion. Risers flows are often simulated by two-fluid model equations coupled with closures developed in the frame the kinetic theory of granular media. However, two-fluid model discretized over coarse mesh with respect to particle clustering size are performed for large units because of limited computational resources. Now, it is well established that meso-scales cancelled out by coarse mesh simulations have dramatic effect on overall behaviour of flows. This study proposed a sub-grid modeling approach for effective drag force and particle stresses which accounts for the effects of unresolved structures on the resolved flows

Hydrodynamic and solid residence time distribution in a circulating fluidized bed: experimental and 3D computational study

Vertical profiles of local pressure, horizontal profiles of net vertical solid mass flux, and residence time distributions (RTD) of the solid phase are experimentally assessed in the riser of a small scale cold Circulating Fluidized Bed of 9 m high having a square cross section of 1111 cm. Air (density 1.2 kg/m3, dynamic viscosity 1.8×10-5 Pa.s) and typical FCC particles (density 1400 kg/m3, mean diameter 70 mm) are used. The superficial gas velocity is kept constant at 7 m/s while the solid mass flux ranges from 46 to 133 kg/m2/s. The axial dispersion of the solid phase is found to decrease when increasing the solid mass flux. Simultaneously, 3D transient CFD simulations are performed to conclude on the usability of the eulerian-eulerian approach for the prediction of the solid phase mixing in the riser. The numerical investigation of the solid mixing is deferred until later since the near-wall region where the solid phase downflow and mixing are predominant is not well predicted in spite of well-predicted vertical profiles of pressure

3D numerical simulation of Circulating Fluidized Bed: comparison between theoretical results and experimental measurements of hydrodynamic

This work was realized in the frame of the European GAYA project supported by ADEME. This paper presents a description of the hydrodynamic into a CFB according to experimental measurements of gas pressure and solid mass flux. These experimental data are compared to three dimensional numerical simulation with an Eulerian approach. The obtained numerical results show that the applied mathematical models are able to predict the complex gas-solid behavior in the CFB and highlight the large influence of the particle wall boundary condition. Indeed, it is shown that free slip wall boundary condition gives a good prediction a solid mass flux profile in comparison with experimental measurements nevertheless a convex shape. Moreover, the numerical solid hold-up is underestimated compared to the experimental data. On the contrary, a no-slip boundary condition improves the profile shape of solid mass flux but highly overestimates its intensity and the solid hold-up. A compromise appears to be a friction particle-wall boundary condition such as Johnson and Jackson (1) but the model parameters have to be chosen very carefully especially the restitution coefficient