 # Fluid Mechanics with Finite Volume Method Teacher Category

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# 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 1

Introduction to Finite volume Method :
Fundamentals of Finite volume methods, different types of finite volume grids

## Session 2

Approximation of surface and volume integrals; interpolation methods

## Session 3

Review of governing equations, Classification of governing equations

## Session 4

Staggered and co-located formulation

## Session 5

Practice 1- 2D mapped Mesh for rectangular pipe

## Session 6

Practice 2- 2D mapped Meshing for Aerofoil.

## Session 7

Grid generation:
Grid generation, creating, updating and managing meshes, Steady diffusion equation on structured meshes

## Session 8

Unsteady diffusion equation on structured meshes, Linear system solvers, finite volume discretization of steady and unsteady diffusion equation

## Session 9

Practice 3- 3D structure mesh of Circular Cylinder

## Session 10

Practice 4- 3D unstructured mesh with primes layers for Aerofoil

## Session 11

Finite volume discretization of convection-diffusion problem

## Session 12

Practice 5- 3D coarse/ medium/ fine sweep mesh for pipe

## Session 13

In compressible flow field calculation with finite volume method:
Navier-stokes equation, Discretization of the Momentum Equation
Navier-stokes equation-ppt

## Session 14

Stream Function-Vorticity approach and Primitive variable approach

## Session 15

Staggered grid and Collocated grid solutions of Navier-stokes equation with finite volume method

## 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
Fluid Kinematics _ppt

## Session 18

velocity and acceleration fields, streamline, streak line, path line

## 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
Fluid dynamics_ppt

## Session 21

Practice- 6. Fluid Analysis of Bernoulli’s equation: Flow in a contracting pipe through CFD simulation

## Session 22

Integration of Euler’s equation along a stream line, Bernoulli’s equation

## Session 23

Flow through Pipes
Reynolds’s Experiment, Laws of Laminar and Turbulent Friction, Introduction Turbulence modeling through Finite volume method
Fluids flow through pipes_ppt

## Session 24

Practice- 7. Fluid Analysis of Laminar flow in 3D Circular Pipe through simulia software

## Session 25

Practice-8. CFD Simulation of the Water Flow Passing Through a Converging Pipe.

## 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.

## Session 28

Flow through small orifice meter, Mouthpiece, Velocity Measurement using Pitot tube, Prandtl tube

## Session 29

Practice-10. CFD Analysis of Fluid flow through Orifice meter

## Session 30

Practice -11.CFD Analysis of Fluid flow through adjustable channel

## Session 31

Flow measurement in pipes-Flow, Venturi Meter, Flow rate Measurement in channel- Weir and Notches

## Session 32

Practice-12. CFD Analysis of Fluid flow simulation through Venturi Meter

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