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 nonNewtonian 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 nonsettling 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 largescale 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 selfcompacting 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 sandwichstructured 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 (twophase liquidsolid 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 nonNewtonian 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 nonNewtonian fluid
 The following formulations are used for most of slurries like coalwater slurries, sand slurries,
1) Density of Slurry Mixture
The density of slurry can be calculated as:
ρ_{m} = 100 / (C_{w}/ρ_{s}) + [(100 – C_{w}) / ρ_{L}]
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 higherconcentration suspensions, the above equation of mixture viscosity is modified as
µ_{m} = µ_{L} [1 + 2.5Φ + 10.05Φ^{2} + 0.00273 exp(16.6Φ)]
Rheology of Slurry

 Understanding the rheological properties of slurries are essential before CFD modeling
 Adding more particles changes the physical properties of slurries like color, density and viscosity
 Effect of volume fraction of particles on viscosity

 The viscosity of slurries changes with a change in particle concentration ; 1) shear thickening, 2) shear thinning
 The effect of particles on rheology of mixture
3. Flow Features of Slurries
 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 EulerianEulerian model (twofluid model) model is commonly used to CFD Modelling the slurry flow
 The in homogeneous EulerianEulerian model (twofluid model) considers continuous (liquid) and dispersed (solid) phases as an interpenetrating continuum.
 The Eulerian – Eulerian model is well suited for highvolume fractions of the dispersed phase (particle concentration) which is averaged over each control volume
 Each phase is governed by similar conservation equations and modeling 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 twophase flow model are given below in brief
 To model slurry flows, volumeaveraged, isothermal, incompressible, and transient NavierStokes 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 particleparticle 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 singlephase 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 threedimensional (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,: noslip condition is imposed on the liquid, but freeslip condition is imposed on the particles.
 Initialization of numerical solution: average volume fractions and mixture velocity are specified as initial conditions.
Numerical Solution

 Pressurevelocity coupling SIMPLE algorithm momentum equations,
 High resolution discretisation scheme : for the convective terms.
 Time step: a fixed timestep of 0.001 s
 The numerical solution was considered to be converged when the residuals of flow variables were less than 10^{−4}
CFD Results:

 Volume fraction of particles is presented for different cross section of pipe
 Effect of inlet volume fraction of particles is presented for different slurries
5. Case Studies of Slurry Flow using CFD Models
5.1 Slurry Flow Of Mineral Deposition
Model assumptions and methodology
In threephase EulerianEulerian model, the phase is defined individually for solid particles, water and air with different velocity fields:

 Continuous phase: water, air
 Disperse phase: solid particles
 Inhomogeneous flow, turbulence is set for three phases
 Each phase is coupled with two other phases through interfacial drag laws
 A powerlaw model or generic yield stress are used to model the slurry flow based on its rheological properties
The slurry mixture viscositc of slurry flow is calculated as follows:

 Set the plastic viscosity is separately defined, hence the mixture viscosity is given by the correlation:
 Liquidphase viscosity is set for water
 The solidphase (sand particles) viscosity is a variable that will change as per its volume of fraction
This multiphase 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
 Mlutiphase model (EulerianEulerian 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
References
 T. N. Ofei, A.Y. Ismai, EulerianEulerian Simulation of ParticleLiquid Slurry Flow in Horizontal Pipe, Journal of Petroleum Eng, Hindawi Pub.( 2016) 5743471
 S. K Lahiri, K.C.Ghanta, Slurry Flow Modelling by CFD , Chem. Ind. Eng., CI &CEO 16 (4) 295−308 (2010)
 S.K.Wee, Y.J. Yap, CFD study of sand erosion in pipeline”, J. Petrol. Sci. Eng., 176, 269–278 (2019).
 B.T. Zengeni, Bingham Yield Stress and and Bingham Plastic Viscosity of Homogenous NonNetwtonian Slurries, (Master Thesis) Cape Peninsula University of Technology, 2016
 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)  CFD Modeling for Slurry Flow Through Bends and Straight Pipe Line, Springer
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.
Hi Sharad, Thank you for the wonderful article. I just wanted to know for ‘slurry flow of mineral deposition’, have you used granular approach for modelling sand. Primary water, secondary – air, sand – is this correct. Which software you have used – CFX/Fluent?