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Fluid Mechanics for Chemical

Engineers

Old and New

by James O. Wilkes

Arthur F. Thurnau Professor

Emeritus of Chemical Engineering

University of Michigan

Wednesday 16 February 2011

wilkes@umich.edu

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Published in 2006

I: Macroscopic FM II: Microscopic FM

773 pages

82 Examples

(incl. 14 CFD)

352 Problems

Two-phase flow

Microfluidics Computational

fluid dynamics

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Two parts, with opportunities

for questions after each.

Macroscopic or relatively large-scalephenomena: basic & simple concepts of mass,

energy, and momentum balances commensuratewith the PE and FE examinations.

Microscopic or small-scale phenomenastarts

with the relatively complicated partial differentialmass and momentum equations of fluid motion.Solutions are often best made by computationalfluid dynamics (CFD) software.

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Part I

Macroscopic Fluid Mechanics

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Characteristic of a Fluid

FluidDeforms continuously when subject to a tangentialor shear force.

Velocity profile: shows how velocity varies with position;note the no-slip condition at each surface.

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StressForce Per Unit Area, F/A

(a)Normal stress = F/A:pressure is the most important case.

(b) Shear stress = F/A: acts tangentially to an area (that due to

viscosity is important example).

(a)

(b)

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Viscosity

ForNewtonian fluids (a broad class), the shear stress = F/A (A =area of plate) is proportional to the velocity gradient du/dy, in

which the constant is the viscosity (with dimensions M/LT):

= du

dy

= V

h

.

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Conservation Law forX= Mass, Momentum, Energy (Only)

The diagram shows a system and transports to and from it. Ignoring the

created and destroyed terms (necessary for reactions but generally not needed in

fluid mechanics), the basic conservation or balance law is:

Xin Xout = XSystem

xin xout=dXSystem

dt.

Or, ifx (lower case) denotes a rate of transferof propertyX, then:

(1)

(2)

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Energy Balance (Bernoullis Equation)

Assumptions:

Steady flow

No work effects (no pump or turbine) Frictionless (OK for short runs of straight pipe)

Incompressible (constant density)

Under these circumstances, the sum of the kinetic energy, potential, and

pressure energy remains constant between points 1 and 2:

u12

2+gz1 +

p1

=u2

2

2+gz2 +

p2

A related form is also available if there are significant work and frictional

effectsespecially useful for pumping and piping problems. Eqn. (1) can also

be divided through by g, so each term has units of length, called either the

velocity, hydrostatic, or pressure head, withHbeing the constant total head.

u12

2g+z1 +

p1

g=H=

u22

2g+z2 +

p2

g

(1)

(2)

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Dynamics of a

distillationcolumn

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End of Part I

Questions?

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Part II

Microscopic Fluid Mechanics

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Representative Computational Fluid

Mechanics (CFD) Software(Usually based on the finite-element, finite-

difference, or finite-volume methods)

Adina

Ansys COMSOL

Flow-3D

Fluent

FlowLab

FloTHERM OpenFOAM

OpenFLOWER

Etc.

For a good overview, see:

http://en.wikipedia.org/wiki/Computational_fluid_dynamics

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Screw Extruder for Increasing the

Pressure of a Polymer Before a Die

h

r

Axis ofrotation

Metering sectionFeed hopper

Barrel

Flights

Exitto die

Screw

Primary feedheating region

W

L0

Compressionsection

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Motion of Barrel as Seen by an Observer

on ScrewCouette (Relative Motion) +

Poiseuille (Pressure-Driven) Flow

x

W

h

Flight axis

Flight

Screw

Barrel

Vx

Vy

V

Flight

z y

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Cross Section between Barrel

(Moving Left) and Screw (Fixed)

p= 0

z

x

y= 0x= 0 2

4

No slip x= 0.1

y= 0.005

1 3No slip No slip = 800 = 500

Vx= - 0.1 A

B

1

2

3

4

Barrel

Screw

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Plots: Arrows, Streamlines, Isobars

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Horace Lamb (18491934)

(to the British Association for the

Advancement of Science, 1932)

I am an old man now, and when I die and go

to heaven there are two matters on which I

hope for enlightenment. One is quantum

electrodynamics, and the other is the turbulentmotion of fluids. And about the former I am

rather optimistic.

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Arrows and Streamlines for Turbulent

Jets

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Turbulent Kinematic Viscosity T

Turbulent Kinetic Energy k

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Flow of a shear-thinning polymer in a die

(a) Extrusion from a pipe forming a tube (b) Rotation, also

exploiting symmetry

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Velocities

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A B

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AB

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l i bl

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x

+

+

+

+

Sternlayer

Potential(negative)

+

+

+

+

+

++

+

+

+

-potential (negative)

Diffuse layer

x= 0

ySolid

surface

Ey

= 0

+

Electric Double Layer

= dV

dy

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x0

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-potentialThe electric potential rises tozero over a very thin electricdouble layer next to the wall

Debye length, D

0

vy vy

=yE

x

VelocityProfile

ElectricPotential

The velocity changes quickly

from zero at the wall to aconstant value everywhere else

0

(constant)

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Electroosmosis (Multiphysics problem:

Navier-Stokes + Conductive Media DC )

Channel Geometry

H= 0.00005,L = 0.0005 m, = 0.1 V

Finite-element Mesh

y

x

y= 0x= 0

2x=L

y = H

1

3

4A

B C

D

Electric insulation

Electric insulation

1 V0 V

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Velocity Vectors (Arrow Plot)

Streamlines

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Electroosmotic Switching1

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Electroosmotic Switching2

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End of Part II

Questions?

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PostscriptWhats the

connection

between thisMemphis juke

box and fluid

mechanics?

Thanks for

your attention!