Five Day ISTE Workshop for Coordinatorson

Computational Fluid Dynamics

March 12 – March 16Indian Institute of Technology Bombay

The National Mission on Education Through ICT(MHRD, Government of India)

Course CoordinatorsBhalchandra Puranik

Atul Sharma

Project CoordinatorProfessor D. B. Phatak

Project ManagerMukta Atrey

Objectives of the Course• Introduction of Fundamentals of Computational

Fluid Dynamics and Heat Transfer. • Level of material: advanced

undergraduate/beginning postgraduate.• Introduction to the methods/algorithms that are

working “behind the screen” when a CFD software operates.– Carefully designed model problems and their

numerical solutions => Development of codes (open source programming environment “Scilab”).

• No CFD software will be introduced.

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

PART IEssentials of Fluid Mechanics

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

Bhalchandra Puranik

Topics• Introduction, some physical properties. • Fluid Dynamics: Integral analysis.• Kinematics of fluid motion.• Fluid Dynamics: Differential analysis.• Some analytical solutions of the Navier-

Stokes equations.• Introduction to numerical solution

methodology – an example using the Finite Difference method.

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

Introduction - 1• Scope of Fluid Mechanics: Equilibrium and

motion of fluids. • Applications: Various branches of Science

and Engineering; Natural phenomena; Sports.

• Fluid*: When at rest, cannot resist a shear force, no matter how small => no static equilibrium under the action of shear force.

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

Introduction - 2• Fluids: Liquids and Gases. • Microscopic (Molecular) or Macroscopic

approaches:– Molecular: “Follow each molecule”; Practically,

statistical methods. – Macroscopic: “Overall/average behavior”; Continuum

model. • Continuum model:

– Continuous distribution of fluid matter and the associated properties.

– Disregard the discrete molecular structure.– Use methods of differential calculus (point-wise smooth

distribution of fluid properties).

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

Introduction - 3• Continuum model:

– Validity of continuum model?– Concept of a “fluid point” => statistically consistent

values of properties (e.g., density) in an infinitesimally small volume.

– The mean free path (l) << Linear dimension of the “fluid point volume” << Characteristic dimension of the problem (L).

– The Knudsen number, Kn = l /L.– If Kn < 0.001 (approx.), continuum model is valid.– Invalid for (i) highly rarefied flows, (ii)

micro/nanoscale flows.

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

Introduction - 4• Important physical properties:

– Pressure (p): molecular origin, compressive in nature.

– Density (r): mass per unit volume. – Specific weight ( = rg): weight per unit volume.– Specific volume (v=1/ r): volume per unit mass.– Dynamic viscosity (m): characterization of the

resistance offered by a fluid in motion to the applied shear forces.

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

Introduction - 5• Dynamic viscosity:

– A simple shear flow: only u=u(y)

– Rate of shear strain (segment PQ):

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

P

Q

yux

y ydyduu

dydu

y

tutydyduu

tt

10

Introduction - 6• Dynamic viscosity:

– t(stress set-up in the fluid to oppose the applied shear stress).

– In general

– If n=1, we have a Newtonian fluid, and

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay

n

dydu

dydu

Introduction - 7• References:

– M. C. Potter, D. C. Wiggert, “Fluid Mechanics”, India Edition, Cengage Learning, 2010. (Chapter 1)

– V. Gupta, S. K. Gupta, “Fluid Mechanics and Its Applications”, 2nd Edition, New Age International, 2011. (Chapter 1)

– R. W. Fox, P. J. Pritchard, A. T. McDonald, “Introduction to Fluid Mechanics”, 7th Edition (SI Version), Wiley India Edition, 2010. (Chapters 1, 2)

Five-Day ISTE Workshop on CFD Bhalchandra Puranik, MED, IIT Bombay