Fluid Mechanics with Finite Volume Method

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Debashree debadatta Behera

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Core Courses

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Fluid Mechanics with Finite Volume Method

Code(Credit) : CUTM1089(2-1-0)

Course Objectives

    •To learn To learn fundamentals of computational methods like FVM for solving linear and non-linear partial differential equations related to fluid dynamics
    •To emphasizes the basic underlying fluid mechanical principles governing energy transfer in a fluid flow systems with their performances in different field of engineering applications.

Learning Outcomes

    • After completion of the course, the students will able to evaluate finite difference/volume schemes on model problems of computational fluid dynamics.
    • Students will learn to develop steady state mechanical energy balance equation for fluid flow systems, estimate pressure drop in fluid flow systems

Course Syllabus

Module I: Introduction to Finite volume Method (6 hrs)
Fundamentals of Finite volume methods, different types of finite volume grids, approximation of surface and volume integrals; interpolation methods, Review of governing equations
Practice 1- 2D mapped Mesh for rectangular pipe
Practice 2- 2D mapped Meshing for Aerofoil.

Module II: Grid generation (6 hrs)
Grid generation, creating, updating and managing meshes, Steady diffusion equation on structured meshes, Unsteady diffusion equation on structured meshes, Finite volume discretization of convection-diffusion problem
Practice 3- 3D structure mesh of Circular Cylinder
Practice 4- 3D unstructured mesh with primes layers for Aerofoil
Practice 5- 3D coarse/ medium/ fine sweep mesh for pipe

Module III: Incompressible flow field calculation with finite volume method(5 hrs)
Navier-stokes equation, Discretization of the Momentum Equation: Stream Function-Vorticity approach and Primitive variable approach, Navier-stokes equation with finite volume method, boundary condition, Reynolds averaged Navier-Stokes equations.

Module IV: Fluid kinematics (2 hrs)
Types of flow, Continuity equation (in one, two& three dimension steady state fluid flow analysis with finite volume method, velocity and acceleration fields, streamline, streak line, path line, velocity potential function and stream function, Rotation and vorticity.

Module V: Fluid Dynamics with Finite volume method (4 hrs)

Lagrangian and Eulerian Approach, Euler’s equation of motion along a stream line for ideal flow, Principle of conservation of energy with finite volume method, Integration of Euler’s equation along a stream line, Bernoulli’s equation
Practice- 6. Fluid Analysis of Bernoulli’s equation: Flow in a contracting pipe through CFD simulation
Module VI: Flow through Pipes ( 5 hrs)

Reynolds’s Experiment, Laws of Laminar and Turbulent Friction, Introduction Turbulence modeling through Finite volume method, Hagen Poiseulle Equation for laminar flow through pipe, Darcy-Weisbach Equation for Turbulent flow through pipe.
Practice- 7. Simulation of Fluid Analysis of Laminar flow in 3D Circular Pipe through
Practice-8. CFD Simulation of the Water Flow Passing Through a Converging Pipe.
Practice-9. Analysis to determine the frictional losses in the pipe.
Module VII: Flow Measurement (5 hrs)
Flow through small orifice meter, Mouthpiece, Velocity Measurement using Pitot tube, Prandtl tube, Flow measurement in pipes-Flow, Venturi Meter, Flow rate Measurement in channel- Weir and Notches
Practice-10. CFD Analysis of Fluid flow through Orifice meter
Practice -11.CFD Analysis of Fluid flow through adjustable channel
Practice-12. Analysis of Fluid flow simulation through Venturi Meter

Text Books:
1.R.K. Bansal, Fluid Mechanics and Hydraulic Machines, Laxmi Publications, ninth edition.

Reference Books:
1.P.N. Modi & S.N. Seth, Hydraulics & Fluid Mechanics, Rajsons Publications Pvt. Ltd, Twentieth Edition

Source of reference; Online sources
1.https://nptel.ac.in/course.html
2.https://nptel.ac.in/courses/112/105/112105218/
3.https://nptel.ac.in/courses/112/105/112105183/
4.https://nptel.ac.in/courses/112/105/112105182/

Session Plan

Session 1

Introduction to Finite volume Method :
Fundamentals of Finite volume methods, different types of finite volume grids
https://www.youtube.com/watch?v=Jgz4gRz4I3o

Session 2

Approximation of surface and volume integrals; interpolation methods
https://www.youtube.com/watch?v=H7X6z5SrQbg

Session 3

Review of governing equations, Classification of governing equations
https://www.youtube.com/watch?v=0j915gwpq4A

Session 4

Staggered and co-located formulation
https://www.youtube.com/watch?v=siBbbLsbh8M

Session 5

Practice 1- 2D mapped Mesh for rectangular pipe
https://www.youtube.com/watch?v=SkQtbEZJVC0

Session 6

Practice 2- 2D mapped Meshing for Aerofoil.
https://www.youtube.com/watch?v=uJCCdT9qV_8

Session 7

Grid generation:
Grid generation, creating, updating and managing meshes, Steady diffusion equation on structured meshes
https://www.youtube.com/watch?v=0j915gwpq4A

Session 8

Unsteady diffusion equation on structured meshes, Linear system solvers, finite volume discretization of steady and unsteady diffusion equation
https://www.youtube.com/watch?v=1woKtFjN-bE

Session 9

Practice 3- 3D structure mesh of Circular Cylinder
https://www.youtube.com/watch?v=o0dPSAHixCI

Session 10

Practice 4- 3D unstructured mesh with primes layers for Aerofoil
https://www.youtube.com/watch?v=PFVVqcc9G2Y

Session 11

Finite volume discretization of convection-diffusion problem
https://www.youtube.com/watch?v=mYXKWAmII10

Session 12

Practice 5- 3D coarse/ medium/ fine sweep mesh for pipe
https://www.youtube.com/watch?v=PFVVqcc9G2Y

Session 13

In compressible flow field calculation with finite volume method:
Navier-stokes equation, Discretization of the Momentum Equation
Navier-stokes equation-ppt
https://www.youtube.com/watch?v=TYkDrmw-0WA

Session 14

Stream Function-Vorticity approach and Primitive variable approach
https://www.youtube.com/watch?v=l-Tz6MHlT1M

Session 15

Staggered grid and Collocated grid solutions of Navier-stokes equation with finite volume method
https://www.youtube.com/watch?v=jnDbVE17Pzg

Session 16

boundary condition, Reynolds averaged Navier-Stokes equations.

Session 17

Fluid kinematics:
Types of flow, Continuity equation (in one, two& three dimension steady state fluid flow analysis with finite volume method
https://www.youtube.com/watch?v=jn_g6cW9r0w
Fluid Kinematics _ppt

Session 18

velocity and acceleration fields, streamline, streak line, path line
https://www.youtube.com/watch?v=r-yA_ifNngg

Session 19

velocity potential function and stream function, Rotation and vorticity.

Session 20

Fluid Dynamics with Finite volume method:
Lagrangian and Eulerian Approach, Euler’s equation of motion along a stream line for ideal flow, Principle of conservation of energy with finite volume method
https://www.youtube.com/watch?v=w2OQF8II-ng
Fluid dynamics_ppt

Session 21

Practice- 6. Fluid Analysis of Bernoulli’s equation: Flow in a contracting pipe through CFD simulation
https://www.youtube.com/watch?v=NcHOf2Jr6OI

Session 22

Integration of Euler’s equation along a stream line, Bernoulli’s equation
https://www.youtube.com/watch?v=9dp0TiysDpk

Session 23

Flow through Pipes
Reynolds’s Experiment, Laws of Laminar and Turbulent Friction, Introduction Turbulence modeling through Finite volume method
https://www.youtube.com/watch?v=3yW_L-xw5sY
Fluids flow through pipes_ppt

Session 24

Practice- 7. Fluid Analysis of Laminar flow in 3D Circular Pipe through simulia software
https://www.youtube.com/watch?v=uZAh_K_wUYo

Session 25

Practice-8. CFD Simulation of the Water Flow Passing Through a Converging Pipe.
https://www.youtube.com/watch?v=ZVpUSzSDD8c

Session 26

Hagen Poiseulle Equation for laminar flow through pipe, Darcy-Weisbach Equation for Turbulent flow through pipe.

Session 27

Practice-9. CFD Analysis to determine the frictional losses in the pipe.
https://www.youtube.com/watch?v=kvNQwb22Om8

Session 28

Flow through small orifice meter, Mouthpiece, Velocity Measurement using Pitot tube, Prandtl tube
https://www.youtube.com/watch?v=29VRA-GjOyY

Session 29

Practice-10. CFD Analysis of Fluid flow through Orifice meter
https://www.youtube.com/watch?v=ZVWF1md8Yeo

Session 30

Practice -11.CFD Analysis of Fluid flow through adjustable channel
https://www.youtube.com/watch?v=sAPiAlELGYY

Session 31

Flow measurement in pipes-Flow, Venturi Meter, Flow rate Measurement in channel- Weir and Notches
https://www.youtube.com/watch?v=vvzTEbp9lrc

Session 32

Practice-12. CFD Analysis of Fluid flow simulation through Venturi Meter
https://www.youtube.com/watch?v=9tbeHejqtKw

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Debashree debadatta Behera

Assistant Professor,Mechanical Engineering Department
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Debashree Debadatta Behera is currently working as an Assistant Professor in the Department of Mechanical Engineering, Centurion University of Technology and Management, Odisha as well as pursuing Ph.D. She had qualified assessment test under Skill Council for Green jobs for Suryamitra and Master Training Programme in Domain Skills and Platform Skills. Her research interests include […]