(149f) Development of a Lift Correlation for Solid-Liquid Flows Using Direct Numerical Simulations

Development of a
lift correlation for solid-liquid flows using direct numerical simulations
(DNS)

The
understanding of the transport of solid particles by fluids is important in
industrial as well as natural processes like biological flows, sediment transport
in rivers, extraction of natural gas using fracking process, and a few more. In
the fracking process, the efficiency of natural gas extraction depends largely
on the placement of solid particles, also known as proppants, in the fractured
rocks. For the proper placement of proppants, it is important to keep these
proppants suspended in liquid in the fracture network near horizontal well and
sediment them at farther distances. The interaction between solid and liquid
plays an important role in the transport of proppants. The main aim of our work
is to gain a fundamental understanding of the liquid-solid flow in narrow
channels using direct numerical simulations(DNS) and develop a large scale
discrete particle model (DPM) for liquid-solid flows which are fundamentally
different from gas-solid flows because of lower density ratios (solid to
fluid), non-negligible lubrication and lift forces on solid particles.

As
an initial step, a fully resolved three-dimensional simulations are carried out
for a solid-liquid flow using Finite Volume Method on a staggered grid. An
accurate fluid-solid coupling is achieved by incorporating the no-slip boundary
condition at particle’s surface by means of an efficient second-order
ghost-cell immersed boundary method. The immersed boundary method is
implemented directly at the level of the discretized fluid equations, unlike
some of the other variants in which the no-slip boundary condition is
implemented using a momentum source term near fluid-solid interface. A fixed Eulerian
grid is used for solving the Navier-Stokes equations and the particle-particle
and particle-wall interactions are implemented using Discrete Element Model
(DEM). The DEM incorporates the soft sphere collision model and a lubrication
force model. In the current implementation, the lubrication force is included
as a sub-grid scale model due to its range of influence on a smaller scale than
the grid size. The particles considered in this study are non-ideal, where the
particle surface has a roughness and the collisions are dissipative. It is
important to note that the DEM model for gas-solid flow ignores the lubrication
force due to higher Stokes number whereas for solid-liquid flows the
lubrication term is dominant and cannot be ignored. Finally, the validated
numerical model will be used to gain more insight in the solid-liquid flow in
narrow channel and use it for developing the closures. The sample simulation of
DNS of fluidization of 24 particles due to lift forces is shown in Figure 1.        

In
the DPM, the fluid-solid momentum exchange is accounted for in the equations
using closure relations for drag force and lift forces. There is a vast amount
of literature investigating the drag force and numerous correlations for drag
force are developed which are dependent on the Reynolds number and void
fraction. However, the momentum exchange due to lift forces is more complicated
due to additional parameters that can vary and therefore more work is needed to
establish a universal correlation. The lift force on a particle is encountered
due to its rotation and the shear rate of the fluid
around it. In a narrow channel, the particles are more likely to be in the
boundary layer region and experience higher shear rates which in turn gives
higher lift force. In DPM, it is not possible to resolve the boundary layer
completely and hence, the lift force due to proximity to wall  should be
included in the correlation. Moreover, the transport of the particles in a
narrow channel also depends on the density ratio (solid to liquid) and particle
size. In this work, numerous DNS simulations were performed to study the
quantitative influence of all the parameters on a lift force for developing a
lift correlation.

Keywords
: Direct
numerical simulations, Immersed boundary method, Solid-liquid flows, Lift
forces, Discrete particle model.