Compressible Flow

Compressible Flow

AERE-311

Previous offerings

Fall 2022, '21, '20, '19, '18, '17

Course Objectives

Sound understanding of fundamentals of compressible fluid flow. Calculate thermodynamic and aerodynamic properties across normal and oblique shock waves and expansion fans. One-dimensional analysis of compressible flow in nozzles and diffusers. 1-D flow with heat addition (Rayleigh flow) and friction (Fanno flow). Solving linearized subsonic and supersonic compressible flow equations.

Outcomes

On completion of the course the attentive student will understand:

• Compute normal shock solutions
• Compute oblique shock solutions
• Compute Prandtl-Meyer expansion solutions
• Compute simple flows using shock expansion methods
• Compute nozzle flows using 1D methods
• Compute straight, constant-area duct flow with heat addition
• Compute 2D subsonic and/or supersonic airfoil lift and/or drag using slender body theory

Syllabus

• Review of thermodynamics
• Governing fluid flow equations
  • continuity, momentum, & energy
• Normal and oblique shock relations
• Prandtl-Meyer expansion fans
• 1-D flow in nozzles and diffusers
• Rayleigh flow (flow with heat addition)
• Linearized subsonic (compressible) and supersonic flow

Textbook and reading mtl.

The suggested reading materials include the following.

• Anderson, J. D. (2016). Fundamentals of Aerodynamics (6th ed.). McGraw Hill. (textbook)
• Anderson, J. D. (2020). Modern Compressible Flow: With Historical Perspective (4th ed.). McGraw Hill.
• James, J. E., & Keith, T. O. (2006). Gas Dynamics (3rd ed.). Pearson.
• Mattingly, J. D., & von Ohain, H. (1996). Elements of gas turbine propulsion. McGraw-Hill New York.

Lecture videos

• Week 1
  • Lecture 1. Introduction and logistics
  • Lecture 2. Fluid compressibility, reference velocity scale, and Mach number
  • Lecture 3. Thermodynamics revision
• Week 2
  • Lecture 4. Thermodynamics revision contd.
  • Lecture 5. Isentropic process; chain rule in partial derivatives
  • Lecture 6. Conservation laws: mass and momentum
• Week 3
  • Lecture 7. No class.
  • Lecture 8. Conservation laws: momentum and energy
  • Lecture 9. Isentropic flow example problem solved using Python
• Week 4
  • Lecture 10. Stagnation and sonic/star states; example problems
  • Lecture 11. Speed of sound and compressibility
  • Lecture 12. Normal shocks and solution procedure
• Week 5
  • Lecture 13. Normal shocks: example problems
  • Lecture 14. Entropy and expansion shocks; Rayleigh Pitot-tube formula
  • Lecture 15. Rayleight Pitot-Tube example problem
• Week 6
  • Lecture 16. Root finding in python; concept of A*; A* variation across a shock
  • Lecture 17. Oblique shocks
  • Lecture 18. Oblique shock theory, Mach wave, theta-beta-Mach relation, example problem
• Week 7
  • Lecture 19. Oblique shocks: example problems
  • Lecture 20. Clarification questions from students
  • Lecture 21. Shock reflections and interactions; examples; shock polars
• Week 8
  • Lecture 22. Prandtl-Meyer expansion fan; example problem; shock-expansion theory
  • Lecture 23. No class.
  • Lecture 24. Shock-expansion theory: lift/drag for a flat plate
• Week 9
  • Lecture 25. Lift/drag for a diamond airfoil
  • Lecture 26. Review of material
  • Lecture 27. Midterm exam
• Week 10
  • Lecture 28. Quasi-1D flow in converging-diverging nozzles
  • Lecture 29. Quasi-1D nozzle flow
  • Lecture 30. Makeup midterm exam
• Week 11
  • Lecture 31. Mass flow rate in a nozzle and choking; example problems
  • Lecture 32. Choked massflow computation; nozzle critical points
  • Lecture 33. Second critical point; shock-in-nozzle condition
• Week 12
  • Lecture 34. Shock-in-nozzle: calculation procedure
  • Lecture 35. Shock diamonds; under- and over-expaded nozzles; supersonic wind tunnels
  • Lecture 36. Converging nozzles; Rayleigh-line flow
• Week 13
  • Lecture 37. Rayleigh-line (R-L) flow: example problems
  • Lecture 38. R-L flow: T-S diagram; why “line”; thermal choking
  • Lecture 39. R-L flow: “diabatic” sonic state, thermal choking and head addition beyond thermal choking
• Week 14
  • Lecture 40. R-L review; intersection of R-L and Fanno flow curves; heat exchange in supersonic flow
  • Lecture 41. Thermal choking and shocks
  • Lecture 42. Linearized velocity potential equation; linearized subsonic flow; wavy wall problem
• Week 15
  • Lecture 43. Lin. supersonic flow: method of separation of variables; lift/drag calculation; comparison with shock-expansion theory
  • Lecture 44. Review - 1
  • Lecture 45. Review - 2
• REVIEW LECTURES
  • Isentropic flow
  • Normal shocks
  • Oblique shocks
  • Nozzle flow
    • Quasi-1D flow
    • Converging nozzles
    • Converging-diverging nozzles
  • Rayleigh-line flow
  • Linearized compressible flow
    • Subsonic flow
    • Supersonic flow