What is Slurry Flow and how to do its CFD Modelling?
By
Dr. Sharad N. Pachpute ( PhD. IIT Delhi)
1. Introduction to Slurry Flows
1.1 What is Slurry Flows?
Slurry is a mixture of solid particles and liquid. Particles can be denser than liquid water
slurry flow is used for transporting solid particles with the liquid being as a carrier medium
The slurry mixture is generally pumped on a device such as a centrifugal pump.
The size of solid particles typically varies in the range of 1 – 100 mm
The particles may settle below a certain transport velocity and the mixture can behave as a Newtonian or non-Newtonian fluid. Depending on the mixture, the slurry may be abrasive and/or corrosive
1.2 Application of Slurry Flow
The slurry flow through pipelines is wide applications in many industries such petroleum, mining, chemical industries and energy and nuclear
Density meter is used to measure the operating density of slurries
Sectional view of the density meter used for slurry flows
Types of Slurries
Different forms of slurries are formed depending on applications
In general, slurries are two types setting and non-settling which are produced as per requirement of industrial applications
1) Coal Slurry
Coal Slurry is a mixture of coal particles, minerals and water
Minerals are mixed based of treatment of chemical processes
2) Food Slurries
Food Slurry is a mixture of food material (from natural or animal extracts) and water
Ingredients are mixed with food and water as per nutrients and deliciousness of final food products
3) Cement slurries
Cement slurry is made of cement, water, and various chemical additives which has a certain density.
Cement slurry is a runny (flow) form of concrete poured into forms for molding and results in the formation of strong construction
It is used around for construction of large-scale building such as large slabs and columns
Cement slurries prepared for home construction
Cement slurries dumped from home construction
4) Slurry due to steel erosion
Slurry erosion is a major problem for slurry handling devices, as it leads to considerable cost caused by failures of devices, replacement of material and high downtime
Slurry erosion from steels depends on slurry properties, service conditions, and material properties
The slurry comprises metal oxides, water and sand particles
5) Sand Slurry
Sand Slurry is also called as a self-compacting form of Controlled Density Fill (CDF) which is mainly used for filling tanks and large voids in excavation.
Sand slurry is made of a small portion of and large volume of water of sand
6) Ceramics Slurry in manufacturing industries
The ceramic slurry is used in forming the mold about the pattern is usually a suspension of insoluble ceramic powders
Ceramic slurry is used for casting and manufacturing industries
A mixture of minerals, water, and additives used in the manufacture of ceramics. A bolus of chewed food mixed with saliva. A mixture of epoxy glue and glass microspheres used as a filler compound around core materials in sandwich-structured composite airframes.
7) Cow Dung Slurries
Cow dung slurries consists of Cow dung (cow pats, cow pies or cow manure) and water and other waste residuals of plants
Cow slurries are used for organic farming as well as for biogas plants
1.3 Complex Multiphase Problem
The slurry flow is multiphase flow problem (two-phase liquid-solid flow)
Understanding of slurry flow is highly complex due to the interactions between the phases as well interactions between the phases and surfaces of pipes
Apart from basic variables of turbulent multiphase flow, other flow parameters such as solids concentration, pipe orientations add extra complexities Hence, CFD models and theories associated with slurry flow have been uncertain. Hence, development of CFD models and experimental understanding of slurry flow in labs are going on in universities and industries
2. Properties of Slurries
Physical Properties of Slurry mixture depend upon composition. Slurries can be Newtonian or non-Newtonian in nature
When the particle concentration of solid within the liquid is less than 10 % by volume, the slurry can consider a Newtonian fluid
When the solid concentration is higher than 10 percent of liquid volume, it is generally considered as a non-Newtonian fluid
The following formulations are used for most of slurries like coal-water slurries, sand slurries,
where:
ρ_{m} =density of slurry mixture (kg/m^{3})
C_{w} = solids concentration by weight (%)
ρ_{s }= density of solid in mixture (kg/m^{3})
ρ_{L} = density of liquid in mixture (kg/m^{3})
2) Volume Fraction
The term volume fraction is represented by the symbol Φ
Φ = C_{v }/ 100
The term volume ratio represents the ratio of the volume of solid (Φ) to the volume of liquid (1- Φ)
Volume Ratio (VR) = Φ / 1 – Φ
where, C_{v} is the concentration of solids by volume (%) and Φ is the volume fraction
3) The concentration of solids
In slurry flows, the concentration of solids particles by volume (C_{v} ) and the its weight ( C_{w) } depend on solid particle density and the mixture density which is given as C_{v} = C_{w}(ρ_{m} / ρ_{s}) where, C_{v} is the solid concentration by volume ( %)
4) Viscosity of slurry mixture
The viscosity of a dilute suspension consisting of solids in a liquid is calculated approximately based on volume fraction Φ and the viscosity of the liquid using the following expression:
µ_{m} = µ_{L }(1 + 2.5Φ)
where, µ_{m} is the viscosity of slurry mixture and µ_{L} is the viscosity of liquid in slurry mixture
The above equation of the mixture viscosity is valid for only to laminar flow consering spherical particles. Also the equation is not valid if solid concentrations exceeds 1 percent by volume
For higher-concentration suspensions, the above equation of mixture viscosity is modified as
Effect of particle concentration profiles on slurry flows are classifies as:
Homogeneous slurry: particles are uniformly distributed
Heterogeneous slurry: particles are not uniformly distributed
Moving bed slurry: the bed formed by particle moves with fluid flow
Stationary bed slurry: the bed formed by particle does not with fluid flow. Such a slurry flow can led to the scaling and blocking of fluid flows
The homogeneous and heterogeneous flows are also called a fully suspended flow
Effect of Pressure gradient on slurries flow
Effect of particle concentration profiles on slurry flows in pipes
4. CFD Modelling of Slurry Flows
For any CFD modelling, understanding mathematical equations are important
The Eulerian-Eulerian model (two-fluid model) model is commonly used to CFD Modelling the slurry flow
The inhomogeneous Eulerian-Eulerian model (two-fluid model) considers continuous (liquid) and dispersed (solid) phases as interpenetrating continuum.
The Eulerian – Eulerian model is well suited for high volume fractions of the dispersed phase (particle concentration) which is averaged over each control volume
Each phase is governed by similar conservation equations and modelling is required for interaction between two phases, turbulent dispersion of particles, and collision of particle with walls.
However, for that complex closure relations are required for the Eulerian – Eulerian model.
The continuity (mass) and momentum equations for two-phase flow model are given below in brief
To model slurry flows, volume-averaged, iso-thermal, in-compressible, and transient Navier-Stokes continuity equations are solved numerically for both liquid and solid (particle) phases
4.1 Continuity Equations
The mass conservation equation without the mass exchange between the liquid and solid phases due to reaction is given as
where h_{l} and h_{s }are the volume fraction of liquid and solid, respectively, and and are the velocity vector of liquid and solid, respectively.
4.2 Momentum Equations
The momentum equations for both liquid and solid phases which considers the interphase momentum exchange term that models the interaction between two phases is given as
Where,
g = gravity term,
p = thermodynamic pressure,
ρ_{l} , ρ_{s} = density of liquid and solid, respectively
M= sum of interfacial forces including drag force and lift force,
τ = the shear stress tensor (for liquid and solid)
The liquid phase and solid phase stress tensors
Bulk solid viscosity
Solid Pressure which represents the solids phase normal forces caused by particle-particle interactions
Here, the first term denotes the particle velocity fluctuations and the second term is due to the particle collisions.
In the above equations, kinetic and collisional components of the solids viscosity are given as
4.3 Interphase Models
Drag Force Model
For spherical particles, the drag force per unit volume is given as
The Gidaspow drag model is used for drag due to solid s particles
Lift Force Model
For spherical solid particles, select the Saffman and Mei lift force model as
4.4 Turbulence Model
Based on the literature, various turbulence models have used in predicting particle concentration profile. However, the k- ε turbulence model is very robust in predicting the particle concentration profile as compared to the other turbulence models
The k- ε turbulence model is well suited for robustness and general purpose of simulations
In multiphase flow, the transport equations for turbulent kinetic energy (k) and dissipation rate (ε ) which are are phase dependent and assume a similar form to the single-phase transport equations
The last terms in each equation are interphase transfer for k and ε
The k- ε turbulence model, the turbulence viscosity is calculated based on the turbulence kinetic energy and dissipation rate
5. Geometry Modelling and Meshing
The three-dimensional (3D) horizontal pipe geometry was modeled
In order to ascertain a fully developed turbulent flow, a hydrodynamic entrance length computed using the following equation
where N_{Re} is the Reynolds number of the liquids and D_{h} is the hydraulic diameter
Boundary and Initial Conditions
Inlet of the pipe: mixture velocity and volume fraction of both liquid and particles phases are specified.
Outlet of the pipe: pressure outlet is specified.
Wall of the pipe,: no-slip condition is imposed on the liquid, but free-slip condition is imposed on the particles.
Initialization of numerical solution: average volume fractions and mixture velocity are specified as initial conditions.
Set the plastic viscosity is separately defined, hence the mixture viscosity is given by the correlation:
Liquid-phase viscosity is set for water
The solid-phase (sand particles) viscosity is a variable that will change as per its volume of fraction
This multi-phase model uses a velocity inlet and pressure outlet for boundary conditions for better convergence.
Free surface profile ; Sand Volume fractions
5.2 Erosion due to Slurry Flow through an Elbow
Using CFD modeling, the particle concentration in pipe sections can be determined in order to find the erosion due to particles
The erosion rate ( mm/s) is predicted using the erosion models
CFD results show that with an increase in the number particles, the erosion rate of pipe increases. We can design the optimum flow rate of slurry and life of pipe
Summary
Slurry flows have many practical applications in nature and industries
Slurry flows cause erosion of pipes and decreases the fluid if concentration of solids is higher or particle size is not uniform
Mluti-phase model (Eulerian-Eulerian model) is used to predict the slurry flows in pipe
Erosion models predict the depreciation of material due to erosion of solid particles
CFD Modeling will help to design the complex slurry flows, how long the pipe or ducts will carry slurry flows within the design limit particles
M. Swamy, N. González Díez, A. Twerd, Numerical modelling of the slurry flow
in pipelines and prediction of flow regimes, Comp.Method Multiphase Flow, WIT Press (2015)
Good article. I wanted to ask if there are research you recommend for civil wastewater models.
In practice, I’ve tried testing some slurries and found conflicting results when it comes to viscosity
(Some samples modeled as shear thinning, some modeled as shear thickening, and some modeled as Binghams plastic).
I’m assuming the cow dung application would be similar, so is there a technique that gets may explain some of the complicated result I found with my testing.
Thanks for your comment.For civil wastewater slurry, we need to know the trend of viscosity which can be obtained from testing the slurry. Then after we will be able implement correctly in CFD modeling. Physical properties like viscosity, flow and geometric parameters are to be consistent for comparison of the results obtained from testing and CFD simulations.
Excellent piece
Thanks for your feedback
Good work. Useful materials Sharad.
Thanks NingeGowda for your feedback
Good article. I wanted to ask if there are research you recommend for civil wastewater models.
In practice, I’ve tried testing some slurries and found conflicting results when it comes to viscosity
(Some samples modeled as shear thinning, some modeled as shear thickening, and some modeled as Binghams plastic).
I’m assuming the cow dung application would be similar, so is there a technique that gets may explain some of the complicated result I found with my testing.
Thanks for your comment.For civil wastewater slurry, we need to know the trend of viscosity which can be obtained from testing the slurry. Then after we will be able implement correctly in CFD modeling. Physical properties like viscosity, flow and geometric parameters are to be consistent for comparison of the results obtained from testing and CFD simulations.