ME 451C:
COMPRESSIBLE TURBULENCE

Stanford University

Mechanical Engineering Department

Last modified Sun June 4, 10:15  AM.

ANNOUNCEMENTS:

INSTRUCTOR: Javier Urzay, Ph.D..
Office: 206 CTR Building. E-mail: jurzay@stanford.edu

LECTURES
Tuesdays and Thursdays, 1:30 PM - 2:50 PM at 380-380Y (Main Quad, Math corner).

OFFICE HOURS
Mondays 4:00-6:00 PM at 206 CTR Building.

COURSE SYLLABUS
(PDF Download)

PREREQUISITES
Familiarity with compressible laminar flows (ME 355) and incompressible turbulence (ME 361), or consent of the instructor.

COURSE DESCRIPTION
Conservation equations. Thermodynamics of ideal gases. Isentropic flows. Crocco-Vazsonyi's equation, creation and destruction of vorticity by compressibility effects. Acoustics and generation of sound by turbulence. Shock waves. Kovasznay's modal decomposition of compressible flow, linear and nonlinear modal interactions, interaction of turbulence with shock waves. Turbulent Mach number. Shocklets. Energetics of compressible turbulence, effects of compressibility on homogeneous turbulence, free-shear flows and turbulent boundary layers. Van Driest transformation, recovery temperature, and shock/boundary layer interaction. Strong Reynolds analogy. Subgrid-scale modeling for compressible turbulence.

REFERENCE TEXTBOOKS (not required)
- A.H. Shapiro, ''The Dynamics and Thermodynamics of Compressible Fluid Flow'', Wiley, 1953.
- H.W. Liepmann & A. Roshko, ''Elements of Gas Dynamics'', Dover, 1957.
- J.D. Anderson, ''Hypersonic and High-Temperature Gas Dynamics'', AIAA, 2006.
- Y.B. Zel'dovich & Y.P. Raizer, ''Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena'', Dover, 2002.
- L.D. Landau & E.M. Lifshitz, ''Fluid Mechanics'', BH, 1959.
- E. Garnier, N. Adams, P. Sagaut: "Large Eddy Simulations of Compressible Flows", Springer, 2009.

EXAMS
Midterm Exam: Tuesday, May 9, in class.
Final Exam: TBA.
Both exams will consist of two parts: i) Short Questions (closed books, closed notes, no calculator), and ii) Problems (open book and open notes, calculator allowed).

GRADING SCHEME
30% Homeworks + 30% Midterm Exam + 40% Final Exam.

REGRADING POLICY
Please contact the instructor for exam regrades.

ACADEMIC INTEGRITY
The Stanford Honor Code will be followed.
https://communitystandards.stanford.edu/student-conduct-process/honor-code-and-fundamental-standard

ACCOMODATIONS FOR STUDENTS WITH DISABILITIES
Requests for appropriate accommodations must be presented to the instructor.

HOMEWORKS
There will be 2 homework assignments. No late homeworks will be accepted.

INSTRUCTOR NOTES

- Lecture Notes (Chs. 1-6) (40 MB, PDF Download)

MIDTERM EXAMS, HOMEWORK ASSIGNMENTS AND SOLUTIONS

Description	Handout	Due date	Solution	Statistics (X/100)
Homework 1	(PDF Download)	Thursday April 27	(PDF Download)	AVE=97.5, STD=2.5
Midterm	(PDF Download)		(PDF Download)	AVE=95.5, STD=3.4
Homework 2	(PDF Download)	Thursday May 18	(PDF Download)	AVE=97.7, STD=1.8
Final Exam				AVE=XX, STD=XX

SUPPLEMENTARY MATERIAL (in chronological order of appearance in class)

- Deakin MA. 2011. GI Taylor and the Trinity test. International Journal of Mathematical Education in Science and Technology, 42(8), pp.1069-1079. (Download link)

- Watts JD. 1968 Flight experience with shock impingement and interference heating on the X-15-2 research airplane. NASA TM X-1669. (Download link)

- Whitham GB., 1952. The flow pattern of a supersonic projectile. Communications on pure and applied mathematics, 5(3), pp.301-348. (Download link)

- Bogdanoff DW. 1983 Compressibility effects in turbulent shear layers. AIAA Journal. 21 :926-7. (Download link)

- Papamoschou D, Roshko A. 1988. The compressible turbulent shear layer: an experimental study. Journal of Fluid Mechanics. 197:453-77. (Download link)

- Abbett M, Moretti G. 1966. A time-dependent computational method for blunt body flows. AIAA Journal 4(12):2136-41. (Download link)

- Plotkin K. Review of sonic boom theory. In 12th Aeroacoustic Conference 1989 (p. 1105). (Download link)

- Wang M, Lele SK, Moin P. 1996 Computation of quadrupole noise using acoustic analogy. AIAA Journal 34, 2247-54. (Download link)

- Nichols J, Lele S, Moin P, Ham F, Bres G, Bridges J. 2012. Large-eddy simulation for supersonic rectangular jet noise prediction: effects of chevrons. In18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference) (p. 2212). (Download link)

- Kovasznay LS. 1953 Turbulence in Supersonic Flow, Journal of the Aeronautical Sciences 20:657-674. (Download link)

- Chu BT, Kovásznay LS. 1958 Non-linear interactions in a viscous heat-conducting compressible gas. Journal of Fluid Mechanics 3:494-514. (Download link)

- Papamoschou D. 1995 Evidence of shocklets in a counterflow supersonic shear layer. Physics of Fluids 7:233-5. (Download link)

- Lee S, Lele SK, Moin P. 1991 Eddy shocklets in decaying compressible turbulence. Physics of Fluids A: Fluid Dynamics 3:657-64. (Download link)

- O'Brien J, Urzay J, Ihme M, Moin P, Saghafian A. 2014 Subgrid-scale backscatter in reacting and inert supersonic hydrogen-air turbulent mixing layers. Journal of Fluid Mechanics 743:554-84. (Download link)

- Pantano C, Sarkar S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. Journal of Fluid Mechanics. 451:329-71. (Download link)

- Samtaney R, Pullin DI, Kosovic B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Physics of Fluids. 13 1415-30. (Download link)

- Vreman AW, Sandham ND, Luo KH. 1996 Compressible mixing layer growth rate and turbulence characteristics. Journal of Fluid Mechanics 320:235-58. (Download link)

- Ribner HS. 1954 Convection of a pattern of vorticity through a shock wave. NACA-TR-1164. (Download link)

- Lee S, Lele SK, Moin P. 1993 Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. Journal of Fluid Mechanics 251:533-62. (Download link)

- Lee S, Lele SK, Moin P. 1997 Interaction of isotropic turbulence with shock waves: effect of shock strength. Journal of Fluid Mechanics 340:225-47. (Download link)