# Advanced Fluid Mechanics & Computational Fluid Dynamics

## What you'll learn

- Provide an introductory overview of Fluid Mechanics tailored to beginner learners, covering fundamental principles and engaging course content.
- Present a comprehensive derivation and detailed explanation of the continuity equation, accompanied by illustrative examples and numerical problem-solving.
- Gain a thorough understanding of the momentum equation, both in its general form and in its differential form, along with practical applications.
- Explore the Navier-Stokes Equation, comprehending its significance and wide-ranging applications in fluid dynamics.
- Acquire a comprehensive understanding of the Reynolds Transport Theorem, including its derivation and practical implications.
- Develop a solid grasp of linear and angular momentum equations and their relevance in fluid mechanics.
- Dive into a detailed examination of the kinematics of various flow types, encompassing a comprehensive exploration of their characteristics.
- Explore the principles of Potential Flow and delve into the concept of superposition, including in-depth discussions of its three types.
- Gain insights into Turbo Machines, including the application of Euler's Equation, analysis of blade angles, and evaluating performance factors.
- Obtain in-depth information about turbines, including their operational characteristics and performance evaluation.
- Familiarize yourself with the core concepts of Boundary Layer, including order analysis over flat plates, turbulent flow over flat plates, the Blasius solution.
- Develop an understanding of External Flow concepts, focusing on topics such as Drag Coefficient and its significance in vehicle aerodynamics.
- Explore the fundamental principles of Airfoil and delve into an analysis of its performance characteristics.
- Gain a comprehensive understanding of advanced concepts in Computational Fluid Dynamics (CFD), including its applications across various industries and fields.

## Requirements

- Basic knowledge of physics and chemistry, including an understanding of fundamental concepts related to forces, motion, energy, and basic chemical principles.
- Proficiency in mathematics, particularly in calculus, differential equations, and algebra, to effectively solve equations and perform mathematical analyses in fluid mechanics.

## Description

Dive deep into the intricate world of Fluid Mechanics and experience the awe-inspiring symphony of fluidic behavior that powers our natural and engineered systems. From the foundational concepts of Newton's laws applied to fluids to the complex calculations needed for engineering problem-solving, this course offers a comprehensive understanding of fluid motion and its critical role in both natural phenomena and man-made inventions. Grasp the nuances of continuity equations, momentum conservation, and the beauty of Navier-Stokes' equations, as they govern fluid flow.

Embark on a journey through the intricacies of turbomachines, exploring their classifications, working principles, and applications. Delve into the dynamics of boundary layers, from their genesis to their effect on the bodies in flow. Engage in the fascinating realm of external flow, uncovering the principles behind drag, lift, and the magnificent designs of airfoils. Finally, stands at the forefront of technological advancement with an introduction to Computational Fluid Dynamics (CFD), exploring the realm of numerical simulations that push the boundaries of engineering capabilities.

This course isn't just about learning theories but bridging the chasm between theory and real-world application. By the end, you will not only understand the mathematics behind fluid motion but will gain a profound appreciation for its relevance in shaping the world around us. Whether you aspire to design advanced aerostructures, engineer efficient transportation systems, or merely satiate an academic curiosity, this course is a key milestone in your journey of discovery and innovation.

**Reference books for this course:**

Fluid Mechanics by Yunus A. Cengel, John M. Cimbala

Fundamentals of Fluid Mechanics, 6th Edition By Munson

COURSE OUTLINE

**Lecture-1 Introduction to Fluid**

The subject of Fluid Mechanics

Laws in the scientific study

Engineering approach of problem-solving

Fluid definition

Newton’s law of viscosity

Newtonian and Non-Newtonian fluid

Problems based on Newton’s law of Viscosity

**Lecture-2 Continuity Equation**

Principle of conservation of mass

Differential and Integral approach

Eulerian and LaGrange's approach

Inventory Equation

Derivation of Continuity equation-Differential approach

Conservation and Non-Conservation Forms of Continuity

Material derivative

Scalar and Vector field

Acceleration field

**Lecture-3 Momentum Equation**

Newton’s Second Law of Motion

Body force

Surface force

Momentum Equation in differential form

Stokes postulate

Navier-Stokes Equation

**Lecture-4 Application of Navier Stokes equation**

N-S equation as governing equation of fluid flow

Application of the N-S equation for a steady and laminar fluid flow between two fixed infinitely long plates.

Velocity profile

Volume flow rate calculation from the velocity profile

Local velocity, average velocity, maximum velocity

Calculating Reynolds Number from the Velocity profile

**Lecture-5 Application of Navier Stokes equation - Couette flow**

The physical meaning of the N-S equation

Fully developed flow

Application of N-S equation for a steady and laminar fluid flow between one fixed and one moving plate-Couette Flow

Applications of Couette flow

**Lecture-6 Reynolds Transport Theorem Derivation**

Control Mass (A System) and Control Volume

Lagrangian and Eulerian Approach

Extensive and Intensive property

Derivation of Reynolds Transport Theorem (RTT)

Interpretation of net flux term of RTT

**Lecture-7 Reynolds Transport Theorem - Continuity Equation**

Reynolds Transport Theorem (RTT)

Deriving Continuity Equation using RTT

Mass flow rate, volume flow rate, and Average speed

Differential and Integral Form of Continuity Equation

**Lecture-8 RTT-Continuity Equation Numericals**

Continuity Equation in Integral Form

Solving numerical problems using Continuity Equation

**Lecture-9 RTT- Linear Momentum Equation**

Reynolds Transport Theorem (RTT)

Deriving Momentum Equation using RTT

Resultant Forces acting on a CV

Momentum accumulation in a CV

Momentum flow through a CV

**Lecture-10 RTT- Angular Momentum Equation**

Reynolds Transport Theorem (RTT)

Deriving Angular Momentum Equation using RTT

Problem-based on Linear and Angular Momentum

RTT for Moving and Deforming CV

**Lecture-11 Kinematics of Flow-Flow Types**

Fluid Flow Visualization- Classics

Streamline

Path-line

Streak-line

Timeline

Software for flow visualization (2dflowvis)

**Lecture-12 Kinematics of Flow- Irrotational Flow**

The motion of fluid Element

Transformation of a fluid element

Angular velocity vector

Vorticity Vector

Irrotational flow field

**Lecture-13 Kinematics of Flow- Stream function**

Visualizing velocity field-Java Applet

Visualizing velocity field- Maple

Stream function

Change in the value of the stream function

Problem with the stream function

Stream function in polar coordinates

**Lecture-14 Kinematics of Flow- Circulation**

Circulation

Relationship between Circulation and Vorticity

Stoke’s theorem

Problem on Circulation

The physical meaning of Divergence of a vector

Circulation and Divergence in Java Applet

**Lecture-15 Potential Flow- Velocity potential function**

Velocity Potential function, φ

Potential flow

Relationship between ψ and φ

Flow net

Velocity potential function in cylindrical coordinates

Velocity Potential function in Java Applet

**Lecture-16 Potential Flow- Basic potential flows**

Uniform flow

Source and Sink flow

Vortex flow

Stream function and Velocity potential function for basic flows

**Lecture-17 Potential Flow- Superposition of potential flows-I**

Superposition of basic potential flows

Doublet

Half body

**Lecture-18 Potential Flow- Superposition of Potential flow-II**

Flow around a cylinder

Flow around a cylinder-Velocity and pressure distribution

Flow around a cylinder-Drag and Lift

Rankine body

Problem with Rankine Body

**Lecture-19 Potential Flow- Superposition of Potential flow-III**

Superposition of basic potential flows

Flow around a cylinder with circulation

Magnus Effect

Problem- Flow around a cylinder with circulation

**Lecture-20 Turbo-machine- Fluid Machines**

Fluid machines classification

Positive Displacement machines

Turbo-machines

Comparison of PDPs and Roto-dynamic pumps

Turbo-machine Classifications

Scope of Turbo-machines

**Lecture-21 Turbo-machine- Euler’s Equation**

One-dimensional flow through an impeller

Velocity triangle

Euler’s equation of turbo-machine

**Lecture-22 Turbo-machine- Blade Angles**

Velocity triangle

Velocity triangle at inlet-assumptions

Effect of blade angle on the head

Typical Characteristic curve of a centrifugal pump

Effect of blade angle on Characteristic curve

**Lecture-23 Turbo-machine- Performance-I**

Problem-Centrifugal blower

Static, Friction, and System head

Pump Losses

Pump Efficiency

Pump Performance Characteristic curves

**Lecture-24 Turbo-machine- Performance-II**

Pump System Curve

Pumps in Series and Parallel

Pump Affinity laws

Pump specific speed

**Lecture-25 Turbo-machine- Turbine**

Turbine

Schematics of hydraulic turbines

Velocity triangles of Turbine

Impulse Turbine

Reaction Turbine

Degree of Reaction

**Lecture-26 Turbo-machine- Turbine Performance**

Pump and Turbine Efficiencies

General Energy Equation

Problem-Turbine

Affinity laws for Turbine

Turbine specific speed

**Lecture-27 Boundary layer- Concept**

Classification of flows

One-dimensional and multi-dimensional flow

Steady and Unsteady flow

Uniform and Non-Uniform flow

Inviscid and Viscous flow

Attached and Flow Separation

Laminar and Turbulent flow

Prandtl-Boundary layer concept

Growth of boundary layer thickness

**Lecture-28 Boundary Layer- Order Analysis over Flat Plate**

Order of Magnitude or Scale Analysis

Order of Magnitude Analysis over a flat plate

Boundary layer thickness as a function of Reynold’s Number

Wall shear stress using Scale Analysis

Skin friction coefficient using Scale Analysis

**Lecture-29 Boundary layer- Blasius solution**

Laminar boundary layer on a flat plate

Blasius solution

Wall shear stress using Blasius solution

Friction coefficient using Blasius solution

Problem- Using Blasius's solution

**Lecture-30 Boundary layer- turbulent flow over a flat plate**

Turbulent flow

Governing Equations in Turbulent Flow

Boundary layer in turbulent flow

The velocity profile in laminar and turbulent flow

Velocity distribution in the turbulent boundary layer

Law of wall

**Lecture-31 Boundary layer- Displacement and Momentum thickness**

Disturbance or Boundary layer thickness

Displacement thickness

Displacement thickness using Blasius solution

Momentum thickness

Momentum thickness using Blasius Solution

The relative amount of displacement and momentum thickness for laminar flow over a flat plate

**Lecture-32 Boundary layer- Approximate solution**

Control Volume analysis for Boundary layer

Von Karman Solution

Von Karman Integral equation

An approximate solution to Laminar boundary layer over a flat plate

**Lecture-33 Boundary layer- Skin Friction Coefficient**

Friction Coefficient for laminar boundary layer

Local and Average skin friction coefficient

Friction Coefficient for Turbulent boundary layer

Friction Coefficient for Mixed boundary layer

Problem- Mixed boundary layer over a flat plate

**Lecture 34 Introduction to EES-Parametric and plotting**

**Lecture-35 External flow- Introduction**

External flow- Application

Forces and Moments on arbitrary shape body

External Flow over a flat plate and cylinder

External flow- Low and High Reynolds's Number flows

Introduction to Open channel flow

External flow characteristics

**Lecture-36 External Flow-Drag and Lift**

The resultant force on a body

Drag and lift Forces

Drag Coefficient

Problem-Drag coefficient

Pressure and Shear stress distribution

**Lecture-37 External flow- Drag Coefficient-1**

Drag and Lift Forces-Alternate Method

The drag coefficient for slender bodies

Problem-Drag coefficient

Factors affecting drag coefficient

**Lecture-38 External flow- Drag Coefficient-2**

The drag coefficient for common geometries

Drafting

Fairing

Drag reduction in nature

Drag reduction in other applications

Experimental measurement of drag coefficient

**Lecture-39 External flow- Drag in Vehicles**

Drag Coefficient of cars-History

Drag and Rolling Resistance on a Vehicle

Power required to drive a vehicle

Problem-Power-Drag and Rolling Resistance

Drag Reduction in Vehicles

**Lecture-40 External Flow-Introduction to Airfoil**

What is Airfoil?

Airfoil types

Airfoil Nomenclature

Aircraft terminologies

Airfoil-Potential flow theory

Minimum Flight Velocity

**Lecture-41 External Flow-Airfoil Performance**

Lift and Drag on Airfoil

Airfoil-Boundary layer theory

Airfoil-Flow separation

Effect of angle of attack

Performance of different Aerofoil

Airfoil with flap

Airfoil at different Mach Number

**Lecture-42 CFD- Introduction**

What is CFD?

CFD Scope and Applications

Role of CFD in Engineering

How CFD works

Practical Steps of Solving Problems in CFD

**Lecture-43 CFD- Finite Difference Method**

Numerical Techniques

Finite difference Method

Forward, Backward and Central Difference

Mixed Derivatives

Problem- Finite Difference Method

Solving problems in CFD using ANSYS-CFX

**Lecture 44 CFD-Geometry and Mesh**

**Lecture 45 CFD-Pre-Solver Solution Post Process (CFX)**

Unlock the secrets of the fluid world and propel your understanding to new heights. Enroll today and embark on an unparalleled journey into the heart of Fluid Mechanics!

## Who this course is for:

- Engineers: The course is designed to cater to engineers from various disciplines who require a strong understanding of fluid mechanics in their respective fields, such as mechanical, civil, chemical, and aerospace engineers.
- Students: This course is suitable for undergraduate and graduate students studying engineering or related disciplines who are seeking to build a solid foundation in fluid mechanics as part of their academic curriculum.
- Professionals: The course also appeals to professionals working in industries where fluid dynamics plays a crucial role, such as automotive, aerospace, energy, and manufacturing. It provides them with an opportunity to enhance their knowledge and skills in fluid mechanics for practical applications.
- Researchers and Academics: Individuals involved in research or academia, including professors, researchers, and postgraduate students, can benefit from the course as it covers fundamental concepts and advanced topics, enabling them to delve deeper into the subject and explore new areas of study.
- Individuals seeking career advancement: Professionals looking to broaden their skill set and increase their career prospects in fields related to fluid mechanics, such as computational fluid dynamics (CFD), hydraulic engineering, or fluid system design, can find this course beneficial in advancing their knowledge and expertise.
- Lifelong learners: The course accommodates individuals with a curiosity for learning and a desire to expand their knowledge base. Lifelong learners who enjoy exploring new subjects and acquiring practical skills can find the course intellectually stimulating and rewarding.

## Instructor

**OZIS Academy** is the platform for struggling university or high school students and professionals who want to improve their skills in the work field as we provide quality and detailed courses. We offer courses from brilliant **Ph.D. Professors** from prestigious Universities who are experts in their relative fields. We have a team of well-experienced, full-time faculty and dedicated staff including talented retired and working University professors. Our mission is to impart the most qualitative education by the way of systematic methodical and scientific approaches.