Advanced Fluid Mechanics

Winter Quarter, 2004-2005

Mechanical Engineering

Stanford University

Stanford, CA

Course outline:

Generalization of classical single component continuum fluid governing equations to multi-component fluid media, with emphasis on effects of energy and chemical non-equilibria. The Duham-Gibbs equation. Indepth discussion of diffusion laws, Onsager's Reciprocity Relation, interesting non-perfect gas effects. Derivation of relevant boundary conditions. Application examples include theory of catalyctic mufflers, sound attenuation by rotational/vibrational relaxation, Ohm's Law for ionized gases, and electrostatic sheaths around electrodes. Coupling of chemical non-equilibrium (reactive gasdynamics) and diffusion (molecular or turbulent). Overview of Renormalization Group (RNG) theory of turbulence. Compressible turbulence in shear layers. Additional topics may include the Transonic Area Rule (Hayes), Sonic Boom (Whitham), Solar Wind (Parker), etc.

If you have suggestions of interesting topics, let me know.

Instructor: Acting Professor Harvey S. H. Lam (

   Questions and/or comments via email is encouraged.

   Office: Room 501C, Building 500

   Phone: 650-483-3870

   Office hour: Tuesday and Thursday, after class. Walk back to my office together. If possible, notify me by email before coming, but it is not necessary if we walk back together.

Lectures: Tuesday/Thursday, 10-11:20AM

   Pigott Hall, Room 260-008 (basement).

Homeworks: Four students will hand in written homework each week (Tuesday), and I will post one or more on this web page. In general, I shall refrain from commenting on the work but I will of course keep a record of your work. Based on the current enrollment, each of you will have this honor three times during the quarter. I encourage all to download the posted answers, and to discuss with the authors your comments/objections/compliments. Electronic homework submission is welcome (PDE files, Word files, etc.).

    At the end of the quarter, all enrolled students are expected to submit ALL the homeworks in one folder to me. It will count 30% of the course grade. The folder will be returned.

Mid-Term and Final: Most probably will be take homes. They contribute 30% and 40% to the course grade.

ME 351B (winter 2003-04) notes.

Week #1: January 4, 6.


   Assignment #1 (due 1/11).

   Supplementary readings: VectorCalculus, Dimensional Analysis, Fluid Stress Tensor.

   Students assigned: Lee Shunn, Matthias Ihme, Bhaskaran Rathakrishnan, Jongwook Joo.

   Homework answers by Lee Shunn.

Week #2: January 11, 13. 

   Equations of state; BZT (Bethe-Zel'dovich-Thompson) gas.

  Assignment #2 (due 1/18)

  Students assigned: Eon Soo Lee, Olivier Desjardins, Perrine Pepiot, Yang Liu.

  Homework answers by Olivier Desjardins. Some comments: (1) The u versus X sketch on page 2 is not qualitatively correct. (2) For problem 5: what happens to the 'shock foot' if the initial right lob is bigger than the initial left lob? (3) For Problem 6: once chooses integration constant to make boundary conditions happy. Here, at upstream and downstream infinity, we want the viscous term to be zero, and we want the left hand side to be zero also. Now, what is the sign of the integration constant? What does the solution look like?

Week #3: January 18, 20.

   Hugoniet Diagram for non-perfect gas. Energy relaxation and bulk viscosity. Introduction to multi-component formulation.

   Assignment #3 (due 1/25).

   Students assigned: Yaser Khalighi, Sangwook Park, Jai Young Ryu, Shravan Hanasoge.

   Homework answers by Yaser Khalighi. Well done.

Week #4: January 25, 27.

   Multi-component diffusion laws, .... and Onsager. This may need more than one week to cover.

   Assignment #4  (due 2/1).

   The bulk of this assignment was written up, and is published in the July 2006 issue of Physics of Fluids.

   Students assigned: Ali Mani, Arthur Rallu, Lee Shunn, Jongwook Joo.

   (The following are visitors or auditors: Matthias Ilme, Luiz Sampaio, Xiaohua Wu, Guowei He, Andre Marta. You are on my mailing list. Welcome.)

   Suplementary readings: Read Coleman and Truesdell---a most important paper. Also A tribute to Clifford Truesdell by Ball and James. Look mainly on page 13 (starting from bottom of page 12). Here are the two seminal Nobel winning papers by Onsager. They are very hard to read. I just want you to see how the original Reciprocity concept got started. Don't spend too much time on them---unless you want to.

  Homework answers by Jongwook Joo.

Week #5: February 1, 3.
   Diffusion Law derivations, boundary conditions, and Onsager Reciprocity Relation.
   Assignment #5  (due 2/8).
    Students assigned: Guillaume Blanquart, Olivier Desjardins, Perrine Pepiot, Yang Liu.
   Homework answers by Perrine Popiot.

Week #6: February 8, 10.
    Ionized gases, Ohm's Law, ambi-polar diffusion, critical mass...
    Assignment #6 (notes only)

   Mid-term this week. All registered enrolled students are expected to hand in the mid-term on 2/15/05.

   Here is the mid-term. Open notes. Work alone. No books.

  Midterm answers by Lam.

Week #7: February 15, 17.

   Reacting flows, chemical kinetics equations, classical methods for reduced chemistry.

   Assignment #7 (due 2/22)

   Students assigned: Yaser Khalighi, Sangwook Park, Shravan Hanasoge, Guillaume Blanquart.

   Homework answers by Lam.

Week #8: February 22, 24.

   Reacting flows, computational singular perturbations.

   Assignment #8 (due 3/1)

   Students assigned: Guillanume Blanquart, Ali Mani, Arthur Rallu, Lee Shunn.

   Supplementary reading: Reduced Chemistry Modelling and Sensitivity Analysis, VKI, 1995.

   Homework answers by Lam.

Week #9: March 1, 3.

   RNG theory of turbulence.

   Assignment #9. (due 3/8); Supplementary notes.

   Students assigned: Jongwook Joo, Guillaume Blanquart, Olivier Desjardins, Perrine Pepiot.

   Supplementary readiing: RNG theory of turbulence.

   Homework answers by Lam.

Week #10: March 8, 10.

   Review, and some fun problems. (see Homework answers for Week #7 posted above). Please bring questions to class.

   No homework assigned. You should use the time to review all your previous homeworks, getting ready to hand in your complete set (with whatever editing you see fit to make) when you hand in the final.

   Supplementary reading: Parker's theory of solar winds.

Here is the open-book/notes take home Final.

Notes on the Final by Lam.

You can pick up your papers from Ms. Deb Michael, secretary to Professor Moin in Building 500, anytime after 2PM, 3/21/2005, Monday.

Thanks for attending my course.   Harvey Lam