# Fluid Mechanics with FVM

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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.

## Course Outcomes

 COs Course outcomes Mapping COs with POs(High-3,Medium-2,Low-1) CO1 Able to gain Knowledge on finite difference/ volume schemes on model problems of computational fluid dynamics. PO1(3) CO3 Able to identify and resolve the problems on steady state mechanical energy balance equation for fluid flow systems, estimate pressure drop in fluid flow systems PO2(3),PO5(1)

## 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 1

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

Study Material: Fundamentals of Finite volume methods ppt

## Session 2

Approximation of surface and volume integrals; interpolation methods

Study material: Finite volume method notes

## Session 3

Review of governing equations

Study material: FVM_notes

## Session 4

Review of governing equations

## Session 5

Practice 1- 2D mapped Mesh for rectangular pipe

## Session 6

Practice 2- 3D mapped Meshing for rectangular grid.

## 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

## Session 9

Practice 3- 3D structure mesh of Circular Cylinder

## Session 10

Practice 4- 3D unstructured mesh of Circular Cylinder

## Session 11

Steady diffusion equation on structured meshes

## 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

Discretization of the Momentum Equation

## Session 15

Navier-stokes equation with finite volume method, boundary condition

## 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

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
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