fluid mechanics and energy transport bien 301 lecture 3 viscosity, flow visualization, flow analysis...

Fluid Mechanics and Energy TransportFluid Mechanics and Energy TransportBIEN 301BIEN 301

Lecture 3Lecture 3 Viscosity, Flow Visualization, Flow Analysis Methods Viscosity, Flow Visualization, Flow Analysis Methods

Juan M. Lopez, E.I.T.Juan M. Lopez, E.I.T.

Research ConsultantResearch ConsultantLeTourneau UniversityLeTourneau University

Adjunct LecturerAdjunct LecturerLouisiana Tech UniversityLouisiana Tech University

12/07/200612/07/2006 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007

ViscosityViscosity

Definition Definition (White 1.7)(White 1.7)

Quantitative measure Quantitative measure of a fluid’s resistance of a fluid’s resistance to flow.to flow.

planeflat s,coordinatecartesian In ,

scoordinate dgeneralizeIn ,2

y

u

g

ut


ViscosityViscosity Newtonian vs. Non-Newtonian FluidsNewtonian vs. Non-Newtonian Fluids

• Newtonian Fluids: Linear Viscosity EquationNewtonian Fluids: Linear Viscosity Equation Examples?Examples?

• Non-Newtonian Fluids: Non-linear Viscosity Eq.Non-Newtonian Fluids: Non-linear Viscosity Eq. Examples?Examples?

• Usually this difference is established as constant viscosity vs. Usually this difference is established as constant viscosity vs. non-constant viscosity. In ALL real fluids, however, viscosity non-constant viscosity. In ALL real fluids, however, viscosity can never be a true constant and varies with T and P.can never be a true constant and varies with T and P.

No-Slip ConditionNo-Slip Condition• For real fluids, it is assumed that at the boundaries, zero slip For real fluids, it is assumed that at the boundaries, zero slip

occurs.occurs.• This is due to jump balance across the interface.This is due to jump balance across the interface.

Temperature BalanceTemperature Balance Momentum BalanceMomentum Balance


Viscosity EffectsViscosity Effects The principal effects of viscosity are divided into two readily The principal effects of viscosity are divided into two readily

visible areas:visible areas:• The boundary layer formationThe boundary layer formation

• TurbulenceTurbulence We’ll cover boundary layer in greater depth later on. For now, We’ll cover boundary layer in greater depth later on. For now,

we’ll focus on the second effect: generation of turbulence.we’ll focus on the second effect: generation of turbulence. We use a dimensionless number to correlate the effects of We use a dimensionless number to correlate the effects of

viscosity on a flow regime: the viscosity on a flow regime: the Reynolds NumberReynolds Number..

v

v

VLVL

where

Re


Viscosity EffectsViscosity Effects

Dimensionless NumbersDimensionless Numbers Many dimensionless numbers in fluid mechanics. We will cover many, many of Many dimensionless numbers in fluid mechanics. We will cover many, many of

them throughout the quarter.them throughout the quarter. Reynolds number relates the kinetic energy to the viscosity.Reynolds number relates the kinetic energy to the viscosity.

• It helps us identify transition into turbulent region, where the viscosity is too great It helps us identify transition into turbulent region, where the viscosity is too great relative to the fluid motion, and orderly movement can no longer occur.relative to the fluid motion, and orderly movement can no longer occur.

Why dimensionless?Why dimensionless?• These are numbers that apply to a flow regime, related to a characteristic dimension.These are numbers that apply to a flow regime, related to a characteristic dimension.• Pick the characteristic dimension that better describes the region you are interested in Pick the characteristic dimension that better describes the region you are interested in

studying, and apply the equation.studying, and apply the equation.



Identify the characteristic dimension for Identify the characteristic dimension for each flow.each flow.



It’s important to think carefully about the characteristic It’s important to think carefully about the characteristic dimension, however it’s not absolutely a perfect science.dimension, however it’s not absolutely a perfect science.

You can pick an alternative characteristic dimension as long as You can pick an alternative characteristic dimension as long as you remain consistent as you compare systemsyou remain consistent as you compare systems



Understanding the meaning of dimensionless numbersUnderstanding the meaning of dimensionless numbers Even though they are quite an alien concept to people outside of Even though they are quite an alien concept to people outside of

fluid mechanics, it is important that you grasp these numbers fluid mechanics, it is important that you grasp these numbers and learn to obtain a “feel” for what these numbers are telling and learn to obtain a “feel” for what these numbers are telling you.you.

Reynolds number:Reynolds number:• High Values, mean a high kinetic energy relative to its ability to flow. High Values, mean a high kinetic energy relative to its ability to flow.

This should cause instability, therefore, we would expect turbulence.This should cause instability, therefore, we would expect turbulence.• Medium values, mean that the kinetic energy is smoothly related to Medium values, mean that the kinetic energy is smoothly related to

its ability to flow. This should cause smoothly changing laminar flow.its ability to flow. This should cause smoothly changing laminar flow.• Low values, mean a low kinetic energy related to its ability to flow. Low values, mean a low kinetic energy related to its ability to flow.

This would be a creeping flow where inertial effects are almost, if This would be a creeping flow where inertial effects are almost, if not entirely, negligible.not entirely, negligible.


Viscosity Effects - ExampleViscosity Effects - Example

A standard example a moving plate with viscous fluid A standard example a moving plate with viscous fluid between the plate and a fixed surface-between the plate and a fixed surface-

Vplate2

Vplate1


Viscosity ChangesViscosity Changes

Viscosity is dependent on temperature and pressure. For Viscosity is dependent on temperature and pressure. For water, we can ignore the effects of pressure.water, we can ignore the effects of pressure.

Viscosity changes as a result of temperature are evident Viscosity changes as a result of temperature are evident in all real fluids. For gases, we have two representations: in all real fluids. For gases, we have two representations: Power Law and Sutherland Law:Power Law and Sutherland Law:

Law SutherlandT

T

LawPower

0

2/3

0

0

0

ST

ST

T

Tn


Viscosity ChangesViscosity Changes

For Liquids, the approximation is as follows:For Liquids, the approximation is as follows:

2

00

0

ln

T

Tc

T

Tba

You can see how this gets much uglier very quickly. You can see how this gets much uglier very quickly. We We really really like idealized fluids. It’s unfortunate we don’t like idealized fluids. It’s unfortunate we don’t

have more of them around.have more of them around.


Thermal EffectsThermal Effects

Similar to viscosity, thermal conductivity Similar to viscosity, thermal conductivity changes the way heat transfer occurs changes the way heat transfer occurs within the fluid.within the fluid.

Thermal conductivity acts on the Thermal conductivity acts on the temperature gradient present in the fluid to temperature gradient present in the fluid to obtain a vector form of heat transferobtain a vector form of heat transfer


Thermal EffectsThermal Effects

The gradient of a property is the partial The gradient of a property is the partial differential of that property with respect to each differential of that property with respect to each of the principal dimensions of the field.of the principal dimensions of the field. Note the Del Operator is a vector operator.Note the Del Operator is a vector operator.

problemty conductivi thermalfor the , ,,

scoordinate dgeneralizeIn , ,,321

321

z

Tk

y

Tk

x

TkzyxTk

g

X

g

X

g

XgggX


Surface TensionSurface Tension

Surface tension arises at the interface Surface tension arises at the interface between a fluid and another system.between a fluid and another system. This system can be another fluid, a solid, or This system can be another fluid, a solid, or

nothing at all.nothing at all. Surface tension is a much more complicated Surface tension is a much more complicated

subject than it will appear to be here. We will subject than it will appear to be here. We will cover a simplified method of studying surface cover a simplified method of studying surface tension.tension.



The coefficient of surface tension, The coefficient of surface tension, ΥΥ, is a , is a measure of force per unit length or energy per measure of force per unit length or energy per unit area present everywhere tangent to the unit area present everywhere tangent to the surface, at the surface.surface, at the surface. Generally, Generally, ΥΥ, changes with the same sign as , changes with the same sign as

temperature, reaching zero at a critical point.temperature, reaching zero at a critical point. When the surface curves, the tension generates a When the surface curves, the tension generates a

pressure difference across the interface.pressure difference across the interface.



The pressure across the surface interface The pressure across the surface interface can be expressed as follows:can be expressed as follows:

bubble hollow a across balance Pressure , 4

sphere a across balance Pressure , 2

cylinder a across balance Pressure ,

Rp

Rp

Rp



WettingWetting When a liquid interacts with a solid surface, there is When a liquid interacts with a solid surface, there is

an angle at that interaction. The magnitude of this an angle at that interaction. The magnitude of this angle defines whether an item wets the solid or not.angle defines whether an item wets the solid or not.• Water wets clean glassWater wets clean glass

Water tends to sheet off clean glass, beads only with Water tends to sheet off clean glass, beads only with imperfections.imperfections.

• Water does not wet waxWater does not wet wax Water beading on the wax job of your car.Water beading on the wax job of your car.



Surface tension also causes the capillary effect.Surface tension also causes the capillary effect. For a cylindrical capillary tube, the height of the fluid For a cylindrical capillary tube, the height of the fluid

column that rises due to the surface tension and the column that rises due to the surface tension and the material wetting the capillary can be found to be as material wetting the capillary can be found to be as follows:follows:

cos2

Rh


CavitationCavitation

Cavitation is a function of vapor pressure. It can Cavitation is a function of vapor pressure. It can be highly damaging.be highly damaging.

Cavitation is described by a non-dimensional Cavitation is described by a non-dimensional parameter, the parameter, the cavitation numbercavitation number.. Which is a function of Pa, ambient pressure, Pv, Which is a function of Pa, ambient pressure, Pv,

vapor pressure, and V, a characteristic velocity.vapor pressure, and V, a characteristic velocity.

21 2V

ppCa va


CavitationCavitation

For most fluids, there is a critical point for For most fluids, there is a critical point for Ca below which the fluid will begin to Ca below which the fluid will begin to cavitate.cavitate. The spontaneous generation and rapid The spontaneous generation and rapid

implosion of gas bubbles in the liquid can implosion of gas bubbles in the liquid can be a highly destructive force.be a highly destructive force.

If not monitored for appropriately, this can If not monitored for appropriately, this can internally destroy a mechanical system.internally destroy a mechanical system.


Speed of SoundSpeed of Sound

Aside from cavitation, we can cause damage to Aside from cavitation, we can cause damage to pipes, ductwork, and cells when we start pipes, ductwork, and cells when we start approaching flows that are a significant fraction of approaching flows that are a significant fraction of the speed of sound in that fluid.the speed of sound in that fluid. This produces damaging shock waves and erosion.This produces damaging shock waves and erosion. This comes from the compressibility effects present in the This comes from the compressibility effects present in the

fluid.fluid. For an ideal gas, the speed of sound is:For an ideal gas, the speed of sound is:

2/1kRTa


Complicated Enough?Complicated Enough?

The answer is…no. Not nearly enough. We have too many The answer is…no. Not nearly enough. We have too many assumptions and simplifications. But this will allow us to begin assumptions and simplifications. But this will allow us to begin working with fluids from a theoretical perspective.working with fluids from a theoretical perspective.

Our problems continue to complicate themselves…viscosity, Our problems continue to complicate themselves…viscosity, then turbulence, now cavitation and compressibility-induced then turbulence, now cavitation and compressibility-induced shock waves…it is apparent that a careful and engineered shock waves…it is apparent that a careful and engineered approach must be taken each and every time we deal with a approach must be taken each and every time we deal with a flow system.flow system.

Enough of the basics for now…how do we DEAL with a flow Enough of the basics for now…how do we DEAL with a flow system? How do we visualize the results? How do we make sense system? How do we visualize the results? How do we make sense of all of this stuff?of all of this stuff?


Flow VisualizationFlow Visualization

One of the most important tools in understanding One of the most important tools in understanding fluid mechanics is being able to visualize what is fluid mechanics is being able to visualize what is going on in our system.going on in our system.

When we visualize these flows, we often use When we visualize these flows, we often use one of a few standard visualization methods:one of a few standard visualization methods:

1) Streamline1) Streamline 3) Streakline3) Streakline 2) Pathline2) Pathline 4)Timeline4)Timeline Note that these are IDENTICAL in steady flow.Note that these are IDENTICAL in steady flow.


Flow VisualizationsFlow Visualizations

StreamlinesStreamlines Everywhere tangent to the velocity vector at a Everywhere tangent to the velocity vector at a

given instant in time.given instant in time.

w

dz

v

dy

u

dx

V

dr



PathlinePathline The displacement of a particle over a defined The displacement of a particle over a defined

period of time, defined by integrating its period of time, defined by integrating its velocity vectors in time to obtain a path.velocity vectors in time to obtain a path.

2

1

2

1

2

1,,

t

t

t

t

t

twdtzandvdtyudtx



StreaklinesStreaklines A streak line is a set of particles that has gone A streak line is a set of particles that has gone

through a particular point in space.through a particular point in space. This is the way experimental work is generally This is the way experimental work is generally

collected.collected.• Injecting hydrogen bubbles, smoke, etc.Injecting hydrogen bubbles, smoke, etc.



TimelinesTimelines The set of particles that form a line in any The set of particles that form a line in any

given instant in time.given instant in time.

Note that for all of these visualizations, Note that for all of these visualizations, streamlines are the “simple” ones to generate streamlines are the “simple” ones to generate analytically. The rest are a result of analytically. The rest are a result of experimentation.experimentation.



Check out the external links on blackboard Check out the external links on blackboard to see some external references on flow to see some external references on flow visualizations.visualizations.

Whole careers are dedicated to the Whole careers are dedicated to the generation of adequate flow visualizations.generation of adequate flow visualizations.

Flow Visualization ExampleFlow Visualization Example


Flow Analysis TechniquesFlow Analysis Techniques

Three primary methods of approaching a Three primary methods of approaching a flow problemflow problem Integral Analysis (Control-Volume Approach)Integral Analysis (Control-Volume Approach) Differential Analysis (Infinitessimal Approach)Differential Analysis (Infinitessimal Approach) Dimensional Analysis (Experimental Study)Dimensional Analysis (Experimental Study)

For ANY of these approaches, we must For ANY of these approaches, we must satisfy the basic laws of mechanics.satisfy the basic laws of mechanics.



Flow Analysis Checklist:Flow Analysis Checklist: Conservation of Mass (Continuity, can also include Conservation of Mass (Continuity, can also include

conservation of species for mixtures)conservation of species for mixtures) Conservation of Momentum (Newton’s second law)Conservation of Momentum (Newton’s second law) Conservation of Energy (First Law of Conservation of Energy (First Law of

Thermodynamics)Thermodynamics) A state relationshipA state relationship Adequate boundary conditions, initial conditions.Adequate boundary conditions, initial conditions. Appropriate assumptions about our flow.Appropriate assumptions about our flow.



AssumptionsAssumptions Our principal assumptions sets come in pairs, to aid in Our principal assumptions sets come in pairs, to aid in

describing our flow condition:describing our flow condition:• Steady or Unsteady?Steady or Unsteady?• Inviscid or Viscous?Inviscid or Viscous?• Incompressible or Compressible?Incompressible or Compressible?• Gas or Liquid?Gas or Liquid?

Once we’ve made our assumptions and followed the analysis Once we’ve made our assumptions and followed the analysis checklist, we are more certain that our results will be meaningful.checklist, we are more certain that our results will be meaningful.

Coupled with White’s 1.13, this is a powerful approach to fluid Coupled with White’s 1.13, this is a powerful approach to fluid mechanics.mechanics.


AssignmentAssignment

HW 3 has been posted on blackboardHW 3 has been posted on blackboard Project Proposals due next time!Project Proposals due next time! Individual project schedules are available Individual project schedules are available

on blackboard.on blackboard.


Questions?Questions?

fluid mechanics and energy transport bien 301 lecture 3 viscosity, flow visualization, flow analysis...

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