ChE 367: Lecture 5

Combest

1/27/2012

Agenda

Announcements

Intro to Fluid Kinematics

Chapter 4

Conclusions about Statics

Chapter 2

Rigid Body Rotation

Rigid Body Motion

Rigid Body Motion

Stationary Static Fluid

Static Fluid with linear motion

*Notes

Rigid Body Motion

Rigid Body Rotation

Stationary Static Fluid

Static Fluid with Rigid Rotation

Gradient operator in cylindrical coordinates

*Notes

Rigid Body Rotation

Magnitude

Rigid Body Rotation

Conclusions about Statics

Fluid Kinematics

The Beginning of Chapter 4

Fluid Kinematics Characteristics of Moving Fluid

Moving Fluids can have….

Pressure gradients

[ 1 ]

Velocity gradients

Fluid Kinematics Characteristics of Moving Fluid

Moving Fluids can have….

Shear Stress

[ 1 ]

Laminar and/or turbulent flow

[ 3 ]

Fluid Kinematics A definition

Kinematics The description and visualization of a fluid’s motion (i.e. velocity and acceleration)

Dynamics The analysis of the forces required to achieve motion

Fluid Kinematics Fields

Scalar, Vector, and Tensor Fields A quantity that is defined as a function of space and time over a particular region.

[ 4 ]

Vector Field Scalar Field [ 5 ]

Fluid Kinematics Eulerian vs. Lagrangian Description

Eulerian Description The frame of reference is stationary in space (i.e. coordinates are independent variables ) and quantities are measured at each point (dependent variables) over time (independent variable ) .

[ 7 ]

Velocity field over x and y

Fluid Kinematics Transport Equations

Eulerian Description

Fluid Kinematics Practical Eulerian Uses

Eulerian Description • Almost all of transport phenomena • Computational fluid dynamics • Spatially inhomogeneous flows (i.e. walls are present) • Anisotropic turbulence

[ 8 ]

Fluid Kinematics Eulerian vs. Lagrangian Description

Lagrangian Description The frame of reference is with respect to a fluid particle and position (dependent variable) changes with time (independent variable).

Fluid Kinematics Transport Equations

Lagrangian Description

?

Fluid Kinematics Practical Lagrangian Uses

Lagrangian Description

[ 6 ]

Coal Particles Solid Particles

Some Announcements

• Start Reading Chapter 4

• HW 2 will be posted this afternoon- Due next Friday

• 3rd checkpoint will be posted as soon as I walk back to my office. Due 1/29/2012

Sources

1. http://research.engineering.wustl.edu/mems/CFDlab/index.html

2. http://claesjohnsonmathscience.files.wordpress.com/2010/10/boundarylayer1.gif

3. http://dspace.mit.edu/bitstream/handle/1721.1/37147/1-061Fall-2002/OcwWeb/Civil-and-Environmental-Engineering/1-061Transport-Processes-in-the-EnvironmentFall2002/LectureNotes/detail/7-lec.htm

4. http://www.openfoam.org/docs/user/cavity.php#x5-40002.1

5. http://tornado.sfsu.edu/geosciences/StormChasing/cases/EN_LN_Patterns/pattern_comparison.html

6. http://criepi.denken.or.jp/jp/energy/gw/activities/simulation/index.html

7. http://www.digitaladdis.com/sk/studentprojects.htm

8. http://www.stanford.edu/group/pitsch/Research/LES.htm