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467147 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.

**Extended Abstract:**File Not Uploaded

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