Slurry flow through pipeline using computational method
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Abstract
The aim of this research internship is to estimate the Head Losses in a pipe loop consisting of a slurry flowing at a specific inlet velocity and thus to find out the feasibility of exporting the slurry through pipelines over large distances. Various solid materials such as minerals can be transported by mixing them in carrier fluid such as water and then removing the water at the outlet. Fluids such as oil can also be transported over large distances. The fluid considered here is water. The slurry considered here is coal ash mixed in water . The software used for simulating the slurry flow through the pipe is Ansys-fluent and Catia software is used for modelling the pipe assembly. The constituents of coal ash are 1)Bottom Ash and 2) Fly Ash . These are used in the production of cement, and also the fly ash can be used for regeneration of mine fields that are left barren after the mining activities. The fly ash neutralizes the acidic mine land when it is spread over it and thus the land can be used for vegetation or other purposes after a period of time. The transportation of this ash from the power stations to the facility of usage is pretty high by roadways and also it takes up a lot of resources such as manpower, diesel etc. Thus, the transportation by pipelines can be a viable option. Computational study appears to be an excellent tool to estimate the pipe flow parameters as it does not demand any sophisticated setup as well as skilled manpower.
Keywords: Head Losses, Slurry, Bottom Ash, Fly Ash, non-newtonian.
INTRODUCTION
Background/Rationale
Statement of the Problems
The underground pipelines can connect the power station to the site of usage which maybe a cement factory or a used mine land. The Head losses in pipelines can be calculated using Ansys simulation and the expenses can be approximated to export the slurry. This research is important in the sense that the simulation will provide the results that can be matched with the practical results for the slurry flow in the pipe assembly. The benefits of using the pipelines will be the decreased expenses to transport the slurry and also the land use will be lesser as the pipelines will be underground mostly rather than the roadways or railways to be laid. Also the consumption of resources that will be required such as fuel for transprtation and manpower, will be reduced . The gap in our knowledge is that the estimated cost of the setting up and the maintainence of pipelines over large distances arestill not known as the simulation and practical are both being done for a pipeloop whose total extent is quite small , only 12m. So the understanding about the flow of slurry in pipes over large distances needs to be improved . Also, in this aspect the pipelines in hilly regions is not considered for now as it will require excess setup and energy .
The conditions that are taken for granted are tht the pipeline can withstand the natural aspects of a particular region such as the climate there and the pressure on the walls of the underground pipes and no maintainence as such is required. It is practically not possible to set up pipelines over a large distance just for the sake of trial run. That is why, Ansys can be used to estimate all the losses and to know the viability of the project.
Objectives of the Research
The objectives of this research are:
✽ To verify whether the Ansys results match with the analytical results for simple cases of Newtonian and non-Newtonian fluid flow .
✽If the results for simulation of the simple cases for the fluid flow matches with the analytical solution, then the simulation results are taken as a reference for comparing with the practical results.
✽Finding out the proportionality in the results when the pipe used are for shorter and larger distances.
✽Finding out the Head losses at different parts of the pipe flow such as the straight pipe, bends, sudden expansion and contraction and the also the losses in the centrifugal pump and the flowmeters.
✽Plotting the losses in the pipe with respect to different inlet velocities and the variation of velocities in the pipe and finding out the optimum velocity for the slurry at the inlet.
✽To compare the results for simple fluid flow in a pipe for Newtonian and non-Newtonian fluids and find out whether the Ansys results matches with the analytical results .
Scope
This model can be economically viable as there is one time investment in laying out the pipelines and also is a model that can help save the resources. The barren mines can be made regenerative again and can be used for vegetative or other purposes. Also, the resources to lay out roadways and railways can be saved. The transportation by the pipes will be faster than the roads and rails. Also, the damage done to the environment in laying out the roadways,railways will be decreased to a large extent in this model. The transportation can be done in any adverse weather condition by the pipelines , which is not possible sometimes if the traditional ways are used.
LITERATURE REVIEW
Information
A number of researchers have been studied to get information on the flow characteristics of slurries . The focus of study in this case was to know about the Head losses in the pipe at varying concentrations of the particles in slurry and various inlet velocities.
Schaanet al.(2000) studied the effect of the particle shape on pipeline loops by taking two pipe loops of diameters 50mm and 150mm for turbulent flow. The concentration of the particles were taken from 15% to45% and the circularity was defined as 0.893, 0.709 and 0.618. It was found that the pipeline friction increases with angularity of the particles.
Gillies et al.(2004) studied the flow of heterogenous slurries of sand having the initial diameters of 0.09 and 0.27 mm in a laboratory test pipe of 0.103m in diameter and having the volume fraction of 0.19 to 0.33 and flow velocity ranging from 0 to 8m/s. The pipeline friction gets lower than expected when the velocity of the slurry is increased.
Verma et al.(2006) studied the pressure drop characteristics of fly ash slurry through 90 degrees bend. They took a pipe loop of 30m and diameter 50mm , solid concentration of 50% to 65% by weight and particle size of 25 micrometers. They observed that the pressure drop increses with the velocity of the fluid and then at higher velocities it becomes constant and the bend coefficient was found to be decreasing with increasing velocities at all concentrations.
El Nahhas et al.(2009) experimentally studied the effect of different particle size of quartz sand on flow characteristics of the slurry. They employed a pipe loop of 18m and diameter of 26.8mm. The sand diameters were taken as 0.2m , 0.7m and 1.4m , and the concentration was varied from 4 to 33%. Friction factor was found out to be directly proportional to the concentration for fine and coarse sand slurry but a little effect of velocity above 5m/s for medium sand slurry.
Liu et al.(2009) experimentally studied the pressure drop characteristics of fluid flow at different regions of pipe .The solids used are two different coal samples with concentration by weight of 57%-59% and 59% to 62% , pipe fittings consisted of bends of diameter 25mm, 40mm and 50mm.,gradual contractions with angle varying from 3degrees to 90 degrees and sudden contraction ratio of 50mm/25mm and 68mm/25mm, It was found that the pressure losses drops to a minimum at gradual contaction initially when the contration angles are small and then it increses with incresing angle. In sudden contraction it was found to be incresing with increasing diameter ratio.
Chandel et al.(2010) studied the pressure characteristics for fly ash and bottom ash at higher concentrations in a pipe loop of diameter 42mm and length 50m. The fly ash and bottom ash were mixed in the ratio 1:4. It was found that the pressure drop increases with increasing solid concentration at certain velocity. At a given concentration the pressure drop decreases with increasing velocity.
Kaushal et al.(2013) simulated the slurry flow by employing the Eulerian model in multiphase modelling. The bend diameter is 53mm . The concentrations are are ranging from 0 to 16.28% of silica sand by volume andand velocity varying from 1.78 to 3.56m/s. The brnd loss velocity decreases as the flow velocity increasesand also as efflux concentration decreases.
Senapati et al.(2013) investigated the experimentally the flow of coarse bottom ash conveyed with finer fly ash with concentration from 62.5% to 67.5% by weight. The pipe diameter was taken as 50mm and the velocity ranging from 0.9m/s to 2.8 m/s. The fly ash an bottom ash were mixed in the ratio of 5:1 . It was observed that the head loss increases with increase in the solid concentration for the flow velocity. The increase in the concentration of the bottom ash resulted in the decrease of head losses due to induction of drag reduction.
Abd Al Aziz et al.(2013) studied the parameters affecting slurry flow through a pipe. They studied the sand and mud slurry flow through a 285 m long pipe assembly and the parameters were found out using the non-diamensionless approach using Reynold's number, Fraude's number, specific gravity, concentration and the particle to pipe diameter. By increasing the Reynold's number from 10907 to 63699 and Fraude's number from 0.5 to 17, they found that the pressure gradient and efficiency of transport were increasing with these numbers. It was found that the flow velocity must be incresed to avoid the blocking of the slurry pipelines . The pressure drop increases and the efficiency of transportation decreases with incresing particle diameter. It was also observed that the higher the value of Reynold's number, higher will be the ability to transport heavier particles.
Kim et al. (2013) studied the flow of sand in water using the Eulerian Granular Multiphase (EGM) model and k-ε turbulent model in ansys (fluent).The specific gravity and the median particle size of sand were taken as 2.65 and 0.54 micrometers respectively. They computationally studied the effect of Reynold's number and delivered concentration by volume on hydraulic gradient. The hydraulic gradient was found to be decreasing with increasing volumetric concentration for smaller values of Reynold's number.
METHODOLOGY
Ansys-Fluent
The method used to resolve the above objectives is by using computational method; Ansys - Fluent.
CATIA is used to model the pipe assembly while Ansys-Fluent is used for simulation and analysis. To verify whether the Ansys results agree with the standard solution , first the 2D analysis of the flow of both Newtonian(in this case- water) as well as non-Newtonian(ash with water) fluids is done and then matched with the analytical solutions. The solutions found to match. The Fluent is then used for 3Dsimulation of slurry through each section of the pipe assembly. The major head losses are found out in two straight sections of the pipes that are each of 50mm and 25mm and each having length 2m. The minor head losses in the pipe assembly are found out in four sections- sudden expansion from 25mm to 50mm, sudden contraction from 50mm to 25mm, losses in the bends of pipe, losses in the centrifugal pump used to pump the fluid at a specific velocity. The losses are plotted with velocity along the pipe , and the inet velocity is varied to find out the variations in the head losses across the pipe and then the most optimum velocity can be chosen for a particular concentration of the coal ash in the water. The concentration of ash in water can also be varied and the most appropriate concentration , that is the maximum concentration of ash with acceptable pressure losses can be estimated. For the convergence of the results, the same concentrations and the velocities must be the parameters that are kept constant while carrying out the practical procedure.
The ansys -Fluent consists of five sections- Geometry, Mesh, Setup, Solutions and Results.
2D analysis
The geometry is a rectangle(section of a pipe) made in the Design Modeller of the Geometry section. The surface is defined and the fluid is defined inside it.
The mesh is generated using a suitable size. For better accuracy, the mesh is made as finer as possible. The mesh size is taken to be 0.01 in this case. For each sectin of the mesh to be uniform , the shape of mesh is chosen as quadrilateral and the face meshing is done. The mesh is then generated. The sections of the pipe are named in this section as- inlet, pipe_wall, Axis and the outlet. Only half pipe is considered in this case.
In the setup, the steady state analysis is used and the Axisymmetric model is used .
For Newtonian fluids' case, the Fluid used in the materials section is water and the material of the pipe is Aluminium. The model used is Viscous(Laminar) . The inlet velocity is given as 0.001m/s for laminar flow and 1m/s for turbulent flow. using the Reynold's number formula. Both the cases are initialized and the calculations are done and the velocity and head loss profiles are found out. These results are then compared with the analytical results obtained using formula for velocity and head losses. The friction factor for finding out the head loss is found out from the Moody's chart(for turbulent flow) and for laminar flow , it is 64/(Reynold's number).
For the Non-Newtonian flow , two approaches are taken into account.
In the first approach the properties of coal ash and water are incorporated in a single fluid that flows through the pipe. All the parameters such as the combined density , flow rate etc are used as input. The velocity is also given at the inlet of the pipe. The model used is k-ω SST model. The rest of the geometry and meshing is kept constant. The velocity and the pressure profiles are obtaied by defining the contours. The variations in velocity with respect to the distance from the axis are plotted and also th gead losses with respect to variation in velocity are plotted at different sections of the pipe.
In the second approach , two phases are defined : one- water and the other coal ash. The coal ash is injected as injections in the discrete phase and its properties are defined in the materials section. The model used is k-ω SST model and the velocity at inlet is given. The velocity profiles at different inlet velocities are found out and the corresponding head losses in the pipe are found out .
3D analysis
In 3D analysis for Newtonian fluid(water),Geometry is a pipe with diameter 50mm and length 2m . The geometry is exported from Catia and then the fluid body and pipe wall is defined . The mesh is generated and is a fine mesh for better velocity and pressure profiles. The model used is viscous(laminar) and the rest of the procedure is same for the 2D analysis of Newtonian flow in pipe which includes clculating the Reynold's number for finding out whether the velocity is in laminar or turbulent regime.The velocity and pressure profiles or both the regimes are plotted and the also the Head losses against velocity is plotted .
For Non-Newtonian fluids the same two aproaches are used as in 2D analysis and the results are oobtained.
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RESULTS AND DISCUSSION
- The analytical results using the formulae for the Head losses in the pipe almost coincides with the Simulation results for the Newtonian flow through the pipe. This result proves that the Ansys simulation matches with the available analytical equations and also Ansys can be used for the simulation of the non-Newtonian flow of slurries such as coal ash mixed in water.
- Thus, the results obtained for slurry flow through the pipe assembly can be considered to be true and can be used for verification with the practical results
- The Images for the results obtained are as follows:
- The image shows the gradually developing laminar velocity profile for Newtonian fluid in the form of a parabola as the analytical also suggests(eq. A5)
- Note: This figure shows half parabola as half pipe is considered. The velocity is thus found out to be maximum near the at the centre, i.e. the axis of the pipe and is 0m/s at the wall of the pipe.
The comparison shows that the velocity is maximum near the centre and 0m/s at the wall of the pipe.
The profile below is of turbulent flow of Newtonian fluid (water) through a half pipe. The velocity near the center is going on getting constant and 0m/s at the wall.
The Comparison shows a slight deviation in the simulation results from the analytical results which results from the mesh size that is taken in the method to perform the simulation. Finer the mesh size more accurate will be the results.
The velocity profile for the non-Newtonian fluid flow:(First approach in methods)
The velocity is zero at the walls of the pipe and is constant near the centre as the profile develops.
Velocity at outlet:
The velocity near the centre is found out to be constant.
Second approach for non-Newtonian fluids as mentioned in the methodology:
Velocity profiles:
Velocity becomes constant near the centre near the outlet.
At the outlet:
The Dynamic and Total pressure profiles :
1) Dynamic Pressure profile:
At oulet:
At inlet:
Full pipe dynamic pressure profile:
These figure can be compared to find out the head losses in the pipe by comparing the dynamic pressure at the inlet and at the outlet. The dynamic pressure decreases as the flow proceeds from the inlet to outlet.
The total pressure profiles:
At outlet:
At inlet:
Full pipe pressure profile:
The Profiles for total pressure shows that the total pressure decreases drastically from inlet to outlet as the flow proceeds.
CONCLUSION AND RECOMMENDATIONS
This project helped to learn Ansys(Fluent) along with Catia . The catia model alongwith the ansys simulation helped to scale down the complexities involoved in finding out the results practically using a setup. The practical procedure is yet to be done and matched with the simulation results. The shortcomings of the project is that the results obtained cannot be used as the final results as there are a number of factors that are not taken into consideration such as the weather conditions in a particular region, the soil type, the pressure on the outer walls of the underground pipes. Also the distance from stations of grneration of material to the destination is variable.
The benefits of the research are it gives an estimated result of the simple slurry flow through the pipe. The Head losses calculated are accurate ,corresponding to the given conditions in the pipe. The practical results can be verified from these simulation results and then the most appropriate result can be used for further applications.
REFERENCES
Schaanet , J.,Sumner, R.J., Gillies , R.J. and Shook , C.A., 2000, The effect of particle shape on pipeline friction for Newtonian slurries of fine particles, The Canadian Journal of Chemical Engineering , 78,717-725
Gillies, R.G. , Shook, C.A. and Xu,J., 2004, Modelling heterogenous slurry flows at high velocities, The Canadian Journal of Chemical Engineering, 82,1060-1065.
Mosa, E.S.,Saleh,A.M., Taha, A.T. , and El Molla, A.M., 2007, A study on the effect of slurry temperature, slurry ph andand particle degradation on rheology, and pressure dropof coal water slurries, Journal of Engineering Sciences ,35(5),1297-1311.
Chandel S.,Seshadri, S., Singh, S.N., 2009, Effect of additive on the pressure drop and rheological characteristics of fly ash slurry at high concentration, Particulate Science and Technology: An International Journal 27, 271-284.
El Nahhas, K. El Hak, N.G., Ryan , M.A.,and El-Sawaf., 2009 , Effect of particle size distribution on the hydraulic transport of settling slurries Thirteenth International Water Technology Conference(IWCTC 13), 463-473
Liu, M.,Duan, Y.F.,2009,Resistance Properties of Coal Water Slurries flowing through local pipe fittings, Experimental Thermal and Fluid Sciences,33,828-837.
Chandel,S. ,Singh, S.N. and Seshadri S.,2010, Transportation of high concentration coal ash slurries through a pipeline, 1(1),1-9.
Verma, S.N, Singh, Seshadri, V. 2006,Pressure Drop for the flow of high concentration solid-liquid mixture across 90degrees horizontal conventional circular pipe bend, Indian Journal of Engineering and Material Sciences, 13,477-483.
Kaushal,D.R. A.,Tomita, Kumar, Y,Kuchii,S,Tsukamoto,H., 2013, Flow of mono-dispersed particles through horizontal bend, International Journal of Multiphase flow,51,71-91.
Senapati, Mishra, B.K., Parida , A.,2013, Analysis of frictionmechanism and homogeneity of suspended load for high concentration of fly ash and bottom ash mixture slurry using rheological and pipeline experimental data, Powder Technology,250,154-163.
Abd Al Aziz,H.I.,Mohamed ,A.I.,2013, A study of factors affecting the transportation of solid-liquid suspensions through pipelines, Open Journal of Fluid Dynamics,3, 152-162.
Kim , C. ,Han , C.,2013, Numerical simulation of Hydraulic Transport of sand- water mixtures in pipelines,Open Journal of Fluid Dynamics,3,266-270.
APPENDIX
Computational Non-Newtonian flow:
(1) Continuity Equation :$\left[\frac{\partial(\rho u)}{\partial x}\right]+\left[\frac{\partial(\rho v)}{\partial y}\right]+\left[\frac{\partial(\rho w)}{\partial z}\right]=0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(A.1)$
(2) Momentum Equation: (2.a) $\left[\frac{du}{dt}\right]=X-\frac1\rho\left[\frac{\partial\rho}{\partial x}\right]+\frac\mu\rho\left[\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2}\right]\;(A.2a)$
(2.b) $\left[\frac{dv}{dt}\right]=Y-\frac1\rho\frac{\partial\rho}{\partial y}+\frac\mu\rho\left[\frac{\partial^2v}{\partial x^2}+\frac{\partial^2v}{\partial y^2}+\frac{\partial^2v}{\partial z^2}\right]\;\;\;(A.2b)$
(2.c) $\left[\frac{dw}{dt}\right]=Y-\frac1\rho\frac{\partial\rho}{\partial z}+\frac\mu\rho\left[\frac{\partial^2w}{\partial x^2}+\frac{\partial^2w}{\partial y^2}+\frac{\partial^2w}{\partial z^2}\right]\;\;(A.2c)$
(3) Navier-Stokes Equation in conservation form for Non-Newtonian fluid :
$\left[\frac{\partial \left(\rho u\right)}{\partial t}\right]+\left[\frac{\partial \left(\rho {u}^{2}\right)}{\partial x}\right]+\left[\frac{\partial \left(\rho vu\right)}{\partial y}\right]+\left[\frac{\partial \left(\rho uw\right)}{\partial z}\right]=-\frac{\partial p}{\partial x}+\frac{\partial}{\partial x}\left[\gamma \nabla v+2\mu \frac{\partial u}{\partial x}\right]+\frac{\partial}{\partial z}\left[\left(\mu \right)\left[\frac{\partial v}{\partial x}+\frac{\partial u}{\partial y}\right]\right]+\frac{\partial}{\partial z}\left[\mu \left[\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x}\right]\right]+\rho {f}_{x}(A.3)$
(4)K-ω SST Model: (4.a): K-Equation: $\frac{\partial(\rho k)}{\partial t}+\frac{\partial(\rho ku)}{\partial x}+\frac\partial{\partial x}\left[(\mu+\frac{\mu_t}{\rho_k})\frac{\partial k}{\partial x}\right]+G_k+G_b-\rho\varepsilon-Y_m+S_{k\;}\;(A.4a)$
(4.b): ω-equation: $\left[\frac{\partial(\rho k\omega)}{\partial t}\right]+div(\rho k\omega u)=\;div\left[\frac\mu{\sigma_\varepsilon}+grad(k\omega)\right]+C_{1\varepsilon}\left[(\frac1kk\omega)\right]2\mu_tE_{ii}E_{ij}-C_{2\varepsilon}\rho\left[\frac{(k\omega)^2}k\right]\;\;\;\;\;(A.4b)$
Analytical Newtonian Flow :
(5) Laminar Velocity Equation: $U(r)=2v(1-\left(\frac rR\right)^2)\;\;(A.5)$
(6)Head loss formula : $\triangle h\;=\;\left[\frac{fl\left(v\right)^2}{2gD}\right]\;\;\;\;(A.6)$
(7)Reynold's number : $Re=\left[\frac{\rho vD}\mu\right]\;\;\;(A.7)$
Non-Newtonian Fluids:
(8) Reynold's number: (8.a) $Re_{pl}=\left[\frac{\rho vD}{k\left({\displaystyle\frac{8v}D}\right)^{n-1}\left({\displaystyle\frac{3n+1}{4n}}\right)^n}\right]\;\;(A.8a)$
(8.b) $Re_{plc}=\left[\frac{404}n\right]\left(n+2\right)^\frac{n+2}{n+1}\left(\frac{4n}{3n+1}\right)^2\;\;(A.8b)$
(8.a)>(8.b) , then the flow is Turbulent, otherwise laminar.
(9)Friction Factors:
(9.a) Laminar flow: 64/Re (A.9a)
(9.b) Turbulent flow: $\frac1{\sqrt f}=\frac4{n^{0.75}}\log\left(Re_{pl}f^\frac{2-n}2\right)-\frac{0.4}{n^{1.2}}$ (A.9b)
ACKNOWLEDGEMENTS
I would like to thank the Indian Academy of Sciences for giving me an opportunity to be a part of the Summer Research Fellowship Progeram 2019. I would also like to thank my guides during the internship duration at IIT GANDHINAGAR- Dr. Prachi Thareja and Mr. Vighnesh Prasad for sharing their valuable experience with me and giving me an opportunity to work for them. Without their guidance this would not have been possible for me. They have been and will be a priceless source of inspiration for me not only for this project but also for my future . They have been a really great host during my period of stay at IIT GANDHINAGAR. Last but not the least , I would like to thank the IIT-GANDHINAGAR administration for providing me with all the facilities like hostel, library , mess and nevertheless, a beautiful surrounding to evolve constantly.
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