Particle‐laden flows in a vertical channel were simulated using an Eulerian–Eulerian, Anisotropic Gaussian (EE‐AG) model. Two sets of cases varying the overall mass loading were done using particle sizes corresponding to either a large or small Stokes number. Primary and turbulent statistics were extracted from these results and compared with counterparts collected from Eulerian–Lagrangian (EL) simulations. The statistics collected from the small Stokes number particle cases correspond well between the two models, with the EE‐AG model replicating the transition observed using the EL model from shear‐induced turbulence to relaminarization to cluster‐induced turbulence as the mass loading increased. The EE‐AG model was able to capture the behavior of the EL simulations only at the largest particle concentrations using the large Stokes particles. This is due to the limitations involved with employing a particle‐phase Eulerian model (as opposed to a Lagrangian representation) for a spatially intermittent system that has a low particle number concentration.
- Award ID(s):
- 1115631
- NSF-PAR ID:
- 10090027
- Date Published:
- Journal Name:
- The ASME 2013 Fluids Engineering Division Summer Meeting
- Page Range / eLocation ID:
- V01CT25A006
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract -
more » « less
Summary In this paper, a three‐dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time three‐dimensional simulations of inertial and turbulent EVP fluids with a large number particles and droplets. This is achieved by combining fast and highly scalable methods such as an FFT‐based pressure solver, with the evolution equation for non‐Newtonian (including EVP) stresses. In this flexible computational framework, the fluid can be modeled by either Oldroyd‐B, neo‐Hookean, FENE‐P, or Saramito EVP models, and the additional equations for the non‐Newtonian stresses are fully coupled with the flow. The rigid particles are discretized on a moving Lagrangian grid, whereas the flow equations are solved on a fixed Eulerian grid. The solid particles are represented by an immersed boundary method with a computationally efficient direct forcing method, allowing simulations of a large numbers of particles. The immersed boundary force is computed at the particle surface and then included in the momentum equations as a body force. The droplets and soft particles on the other hand are simulated in a fully Eulerian framework, the former with a level‐set method to capture the moving interface and the latter with an indicator function. The solver is first validated for various benchmark single‐phase and two‐phase EVP flow problems through comparison with data from the literature. Finally, we present new results on the dynamics of a buoyancy‐driven drop in an EVP fluid.
-
more » « less
We develop a formally high order Eulerian–Lagrangian Weighted Essentially Nonoscillatory (EL‐WENO) finite volume scheme for nonlinear scalar conservation laws that combines ideas of Lagrangian traceline methods with WENO reconstructions. The particles within a grid element are transported in the manner of a standard Eulerian–Lagrangian (or semi‐Lagrangian) scheme using a fixed velocity
v . A flux correction computation accounts for particles that cross thev ‐traceline during the time step. Ifv = 0, the scheme reduces to an almost standard WENO5 scheme. The CFL condition is relaxed whenv is chosen to approximate either the characteristic or particle velocity. Excellent numerical results are obtained using relatively long time steps.The
v ‐traceback points can fall arbitrarily within the computational grid, and linear WENO weights may not exist for the point. A general WENO technique is described to reconstruct to any order the integral of a smooth function using averages defined over a general, nonuniform computational grid. Moreover, to high accuracy, local averages can also be reconstructed. By re‐averaging the function to a uniform reconstruction grid that includes a point of interest, one can apply a standard WENO reconstruction to obtain a high order point value of the function. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 651–680, 2017 -
Formation, expansion, and breakage of bubbles in single bubble and freely bubbling fluidized beds were studied using an improved hybrid Lagrangian-Eulerian computational fluid dynamics (CFO) approach. Dense Discrete Phase Model (DDPM) is a novel approach to simulate industrial scale fluidized bed reactors with polydispersed particles. The model uses a hybrid Lagrangian-Eulerian approach to track the particle parcels (lumping several particles in one computational cell) in a Lagrangian framework according to Newton's laws of motion. The interactions between particles are estimated by the gradient of solids stress solved in Eulerian grid. In this work. a single bubble fluidized bed and a freely bubbling fluidized bed were simulated using DDPM coupled with kinetic theory of granular flows (KTGF). The solid stress was improved to include both tangential and normal forces compared to current hybrid methods with the consideration of only normal stress or solid pressure. The results showed that solid pressure (normal forces) as the only contributor in solid stress would lead to over prediction of bubble size and overlooking of bubble breakage in a single bubble bed. Also, the results showed the improved model bad a good prediction of bubble path in a freely bubbling bed compared to solid pressure-based model. It was shown that increasing the restitution coefficient increased the particle content of the bubbles and it lead to less breakage during the formation of the bubble. The probability of formation of bubbles was compared with experimental results and solid stress model showed less discrepancies compared to the solid pressure-based model.more » « less
-
more » « less
Abstract A new modeling methodology for ripple dynamics driven by oscillatory flows using a Eulerian two‐phase flow approach is presented in order to bridge the research gap between near‐bed sediment transport via ripple migration and suspended load transport dictated by ripple induced vortices. Reynolds‐averaged Eulerian two‐phase equations for fluid phase and sediment phase are solved in a two‐dimensional vertical domain with a
k ‐ε closure for flow turbulence and particle stresses closures for short‐lived collision and enduring contact. The model can resolve full profiles of sediment transport without making conventional near‐bed load and suspended load assumptions. The model is validated with an oscillating tunnel experiment of orbital ripple driven by a Stokes second‐order (onshore velocity skewed) oscillatory flow with a good agreement in the flow velocity and sediment concentration. Although the suspended sediment concentration far from the ripple in the dilute region was underpredicted by the present model, the model predicts an onshore ripple migration rate that is in very good agreement with the measured value. Another orbital ripple case driven by symmetric sinusoidal oscillatory flow is also conducted to contrast the effect of velocity skewness. The model is able to capture a net offshore‐directed suspended load transport flux due to the asymmetric primary vortex consistent with laboratory observation. More importantly, the model can resolve the asymmetry of onshore‐directed near‐bed sediment flux associated with more intense boundary layer flow speed‐up during onshore flow cycle and sediment avalanching near the lee ripple flank which force the onshore ripple migration.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/FEDSM2013-16567
