ME 522, Spring 2019
Foundations of Fluid Mechanics II

Prepared by Professor J. M. Cimbala, Department of Mechanical Engineering at The Pennsylvania State University
Latest revision, 26 August 2024

[Syllabus]
[Equations]
[Exams]
[Grades]
[Instructor]
[References]
[TA]
[Textbook]
[Videos]
Week
Dates
Lecture material
Homework
Exams
Week 1
01/07-01/11
Chapter 10 - 2-D laminar boundary layers (continued from ME 521): Falkner-Skan flows; free shear flows
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Week 2
01/14-01/18
Chapter 10 - Axisymmetric laminar boundary layers: introduction, equations; Mangler transformation; Three-dimensional laminar boundary layers: introduction, coordinate systems; secondary flow
Cool spinning ice disk in Maine!
HW 1
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Week 3
01/21-01/25
Chapter 11 - Instability: introduction; linear stability theory; method of normal modes
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Week 4
01/28-02/01
Chapter 11 - Instability (continued): brief summary of various flow instabilities; begin the Benard problem
Hadley cells in earth's atmosphere
Cool current global map of wind
NOAA article about polar vortex.
See also NOAA polar vortex picture and compare to Taylor instability in narrow gap
HW 2
R_K_for_Blasius_BL.m
Blasius_RK_in_Excel.xlsx
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Week 5
02/04-02/08
Chapter 11 - Instability (continued): the Benard problem (continued)
Benard Marginal Stability Curve, Matlab code
HW 3
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Week 6
02/11-02/15
Chapter 11 - Instability (continued): locally parallel flows; Squire s theorem; The Orr-Sommerfeld equation
Youtube video: NSF Instability film with corrected sound
Video: Interacting vortex rings with a cool instability
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Midterm Exam 1, in class
Friday, February 15
Week 7
02/18-02/22
Chapter 11 - Instability (continued): examples of Orr-Sommerfeld "thumb" curves; The Rayleigh equation (inviscid approximation of Orr-Sommerfeld equation)
National Committee for Fluid Mechanics Films: Instability (film with corrected sound)
HW 4
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Week 8
02/25-03/01
J. M. Cimbala's PhD thesis - Instability of a far wake; Begin to discuss Turbulence, The Final Frontier: introduction - the characteristics & features of turbulence, definitions
Cimbala, Nagib, Roshko 1988 JFM paper: Far Wakes
Youtube video, T-S waves and transition to turbulence
Youtube video, Intro to turbulence in 5 minutes
HW 5
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Spring Break
03/04-03/08
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Week 9
03/11-03/15
Chapter 12 - Turbulence (continued): definitions, etc. (how to describe turbulence); Turbulence statistics; turbulent kinetic energy; homogeneous turbulence and isotropic turbulence; Reynolds decomposition and introduce the Reynolds stress
Video: turbulence in a box, from http://gfs.sourceforge.net/examples/examples/forcedturbulence.html
HW 6
hw_06_Problem_02_Benard_POST.xlsx
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Week 10
03/18-03/22
Chapter 12 - Turbulence (continued): Reynolds stress and the turbulence closure problem; Kolmogorov s contributions; Energy scales and the energy cascade
YouTube video: Smoke rings and turbulent scales
HW 7
hw_07_Problem_02_post.xlsx
posted 03/18/2019
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Week 11
03/25-03/29
Chapter 12 - Turbulence (continued): Fun with Kolmogorov microscales (movie making, etc.)
National Committee for Fluid Mechanics Films: Turbulence
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Midterm Exam 2, in class
Friday, March 29
Week 12
04/01-04/05
Chapter 12 - Turbulence (continued): the turbulent scales problem and why we need turbulence models; Turbulence Models: introduction to turbulence modeling; Classification of turbulence models: zero-equation models, one- and two-equation models, ASM models, 7-equation models; URANS, LES, DES, PANS, etc. models; Intro to mixing length and eddy viscosity concepts
Exaflop computer coming soon!
World's fastest computer
HW 8
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Week 13
04/08-04/12
Chapter 12 - Turbulence Models (continued): the Boussinesq eddy viscosity model, wall treatment, details about and equations for "half"-, one-, and two-equation models
HW 9
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Week 14
04/15-04/19
Chapter 12 - Turbulence Models (continued): RSM models; Turbulent Flow Solutions: turbulent channel flow; Turbulent boundary layer
Turbulence_Model_Summary_Chart.pdf
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Week 15
04/22-04/26
Chapter 12 - Turbulent Flow Solutions (continued): free shear flows: jets, wakes, and mixing layers
HW 10 - Due Wednesday 04/24. No late HW 10 accepted after 5:00 p.m. on Friday
Marasli_normalized_wake_data_POST.txt
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Finals Week
04/29-05/03
The final exam is scheduled for:
Monday April 29, 6:50-8:40 pm in 214 Wagner Building
OPTIONAL HW 11
Final Exam
BYOS