Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer
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Transcript of Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer
Fluid Mechanics and Energy TransportFluid Mechanics and Energy TransportBIEN 301BIEN 301
Lecture 16Lecture 16Compressible Flows Continued – Friction in DuctsCompressible Flows Continued – Friction in Ducts
Juan M. Lopez, E.I.T.Juan M. Lopez, E.I.T.
Research ConsultantResearch ConsultantLeTourneau UniversityLeTourneau University
Adjunct LecturerAdjunct LecturerLouisiana Tech UniversityLouisiana Tech University
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Compressible Duct Flow with Compressible Duct Flow with FrictionFriction
Expanding on Nozzle Analysis Expanding on Nozzle Analysis (White 9.7)(White 9.7)
Basic AssumptionsBasic Assumptions• Steady 1D adiabatic flowSteady 1D adiabatic flow• Ideal Gas with constant Cp and CvIdeal Gas with constant Cp and Cv• Constant-area straight ductConstant-area straight duct• Wall shear stress correlated with a Darcy friction factor.Wall shear stress correlated with a Darcy friction factor.
Like a moody analysis but with very large changes in Like a moody analysis but with very large changes in Kinetic Energy, Enthalpy, and pressure.Kinetic Energy, Enthalpy, and pressure.
Often called “Fanno Flow”Often called “Fanno Flow” AN IMPORTANT CLARIFICATION: For this chapter, * AN IMPORTANT CLARIFICATION: For this chapter, *
denotes a critical (sonic point) property.denotes a critical (sonic point) property.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Fanno FlowFanno Flow
From control volume analysis, we end up with the basic From control volume analysis, we end up with the basic relationship between mach number and flow:relationship between mach number and flow:
D
dxf
Ma
MakMak
Ma
dMa2
2
22
2
1
121
1
This is already a separated variables form of the equation, which we This is already a separated variables form of the equation, which we can integrate to obtain the following. (Tabulated in table B.3 in can integrate to obtain the following. (Tabulated in table B.3 in textbook):textbook):
2
2
2
2
12
1ln
2
11
Mak
Mak
k
k
Mak
Ma
D
fL
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Fanno FlowFanno Flow
This relationship leads to a few simple This relationship leads to a few simple relationships shown as follows:relationships shown as follows:
PropertyProperty SubsonicSubsonic SupersonicSupersonic
pp DecreasesDecreases IncreasesIncreases
ρρ DecreasesDecreases IncreasesIncreases
VV IncreasesIncreases DecreasesDecreases
p p 00, , ρρ00 DecreasesDecreases DecreasesDecreases
TT DecreasesDecreases IncreasesIncreases
MaMa IncreasesIncreases DecreasesDecreases
EntropyEntropy IncreasesIncreases IncreasesIncreases
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Fanno FlowFanno Flow
Entropy changes Entropy changes tend towards the tend towards the maximum entropy maximum entropy change at Ma = 1.change at Ma = 1.
Equations 9.66a-d Equations 9.66a-d are used to are used to calculate the ratios calculate the ratios between critical between critical throat pressures throat pressures and entrance or and entrance or reference reference pressures.pressures.
1121
2
0
0
0
0
22
2
21
2
2
21
22
1
121
12
1
1
121
12
11
kk
k
xMak
Map
p
Mak
k
a
a
T
T
k
Mak
MaV
V
Mak
k
Map
p
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Choking FlowChoking Flow
An interesting propertyAn interesting property The theory presened thus far has one interesting The theory presened thus far has one interesting
consequence: no matter what inlet Ma, in an adiabatic consequence: no matter what inlet Ma, in an adiabatic flow the downstream flow shall ALWAYS trend flow the downstream flow shall ALWAYS trend towards Ma = 1.towards Ma = 1.
Are flows truly adiabatic?Are flows truly adiabatic?• No, but for many flow regime ranges this is a good No, but for many flow regime ranges this is a good
approximation.approximation.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Additional Fanno Flow Additional Fanno Flow PropertiesProperties
Minor Losses in Compressible FlowMinor Losses in Compressible Flow
Isothermal flow with friction: Long pipelinesIsothermal flow with friction: Long pipelines
Mass Flow for a given pressure drop in an adiabatic ideal gas:Mass Flow for a given pressure drop in an adiabatic ideal gas:
tcoefficien loss static ,
22
22
21
Vp
ppK s
point chokingat is ' where''
;1
'2
1
21 kMa
V
V
kMap
p
2
220
21
20
1
2
2
1
1
2
2
1
12
12
Vka
Vka
p
p
T
T
p
p
V
V
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Adding Heat to the EquationAdding Heat to the Equation
This course is also energy transport. What This course is also energy transport. What happens when we add heat to our flow happens when we add heat to our flow problem?problem?
21
1
2
1
2
11
22
1
2
T
T
Ma
Ma
aMa
aMa
V
V
See equations 9.78a-e for the additional See equations 9.78a-e for the additional Ma number relationships.Ma number relationships.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Additional ItemsAdditional Items
Remember, we are skipping shock wavesRemember, we are skipping shock waves Read the choking flow due to heat example in the text Read the choking flow due to heat example in the text
(E9.15)(E9.15)
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Chapter 9 HomeworkChapter 9 Homework
DUE 2/22/2007 - ReminderDUE 2/22/2007 - Reminder
P9.11P9.11P9.43P9.43P9.78P9.78P9.88P9.88
EC: P9.114EC: P9.114
Due with the Ch. 7 and Ch. 8 HW.Due with the Ch. 7 and Ch. 8 HW.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
REVIEW FOR FINALREVIEW FOR FINAL
Final Exam on Tuesday, Feb. 27Final Exam on Tuesday, Feb. 27thth
Chapters 6, 7, 8, 9. Your write-ups on Ch. 5 Chapters 6, 7, 8, 9. Your write-ups on Ch. 5 will be all I need from that chapter.will be all I need from that chapter.
Same two-part format: closed book and open Same two-part format: closed book and open book.book.
NO DOCUMENTS OTHER THAN TEXBOOK NO DOCUMENTS OTHER THAN TEXBOOK ALLOWED FOR THIS EXAM. ALLOWED FOR THIS EXAM. • I am writing the exam to ensure this is all you will I am writing the exam to ensure this is all you will
need.need.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
REVIEW FOR FINALREVIEW FOR FINAL
Additions to the format:Additions to the format: Closed Book PortionClosed Book Portion
• Mixture of True/False, Short Answer, Fill-In-The-Mixture of True/False, Short Answer, Fill-In-The-Blank, and Multiple ChoiceBlank, and Multiple Choice
Open Book PortionOpen Book Portion• Multiple ChoiceMultiple Choice
Showing work gets you partial credit even if you select Showing work gets you partial credit even if you select the wrong answer. the wrong answer.
Showing irrelevant work is the same as showing NO Showing irrelevant work is the same as showing NO work, so do work the stuff out. work, so do work the stuff out.
Guessing will NOT help you. You will get a zero.Guessing will NOT help you. You will get a zero.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
REVIEW FOR FINALREVIEW FOR FINAL
Concepts we will NOT be covering:Concepts we will NOT be covering: Ch. 6Ch. 6
• 6.5, Moody Charts, Details on flowmeters, 6.5, Moody Charts, Details on flowmeters, correction factors.correction factors.
Ch. 7Ch. 7• AirfoilsAirfoils
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
REVIEW FOR FINALREVIEW FOR FINAL
Concepts we will NOT be covering:Concepts we will NOT be covering: Ch. 8Ch. 8
• 8.3-8.78.3-8.7 Ch. 9Ch. 9
• 9.5, 9.9, 9.109.5, 9.9, 9.10
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
REVIEW FOR FINALREVIEW FOR FINAL
Will Probably be 10 or so questions on Will Probably be 10 or so questions on Part 1Part 1
2-3 Questions on Part 2.2-3 Questions on Part 2. You may show up at 7:30 am if you wish.You may show up at 7:30 am if you wish.
The exam will not be longer than the rest, but The exam will not be longer than the rest, but it is the final, so you may have some extra it is the final, so you may have some extra time to work on it if you feel you want to get time to work on it if you feel you want to get here earlier.here earlier.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
REVIEW FOR FINALREVIEW FOR FINAL
I will only be handing back your final grade I will only be handing back your final grade via blackboard. If you want your exam, via blackboard. If you want your exam, you’ll have to get in touch with me next you’ll have to get in touch with me next quarter.quarter.
2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007
Questions?Questions?