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.

Course Outcomes

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- 3D mapped Meshing for rectangular grid.

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
Practice 3- 3D structure mesh of Circular Cylinder
Practice 4- 3D unstructured mesh of Circular Cylinder
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, Navier-stokes equation with finite volume method, boundary condition.

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

Study Material: Fundamentals of Finite volume methods ppt

Session 2

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

Study material: Finite volume method notes

Session 3

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

Study material: FVM_notes

Session 4

Review of governing equations
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- 3D mapped Meshing for rectangular grid.
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
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 of Circular Cylinder
https://www.youtube.com/watch?v=PFVVqcc9G2Y

Session 11

Steady diffusion equation on structured meshes
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

Discretization of the Momentum Equation
https://www.youtube.com/watch?v=l-Tz6MHlT1M

Session 15

Navier-stokes equation with finite volume method, boundary condition
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

Study Material:Fluid kinematics and dynamics

Session 19

velocity potential function and stream function, Rotation and vorticity.

Study material: Fluid kinematics and dynamics

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