Compressibility and High-Speed Flow




3L-0T-0P-0A (9 Credits)


Pre-requisite: Thermodynamics and Fluid mechanics


The emphasis will be on physical understanding of compressible flows, shock waves dynamics, compressible turbulence, and analytical techniques.

Course content

The fundamental of compressible flow, conservation laws, steady and unsteady inviscid subsonic and supersonic flows, method of characteristics, small-perturbation theories, linearized velocity potential flow, shock waves dynamics and wave structure, Prandtl-Meyer function, Reflected and intersecting shocks, self-similar compressible flows, compressible flows in ducts with area changes, friction and heat addition, compressible boundary layer, viscous and compressibility effects, shock wave-boundary layer interactions, turbulent flows, numerical techniques, transonic and hypersonic flows, high-temperature flow.

Total number of lectures: 43

Lecturewise breakup

1. Review of fundamentals;Fluid mechanics and thermodynamics: 3 Lectures

  • Definition of compressible flow, Conservation laws

  • Review of thermodynamics and entropy

  • Mach angle, subsonic, supersonic, and hypersonic flows

2. Review of steady and unsteady one-dimensional gas dynamics : 6 Lectures

  • Isentropic flow, flow with heat addition, flow with friction

  • Normal shock waves, Rankine-Hugoniot relations

  • Moving normal shock

  • Characteristic equations and Numerical methods

3. Two-dimensional gas dynamics: 5 Lectures

  • Oblique shocks, shock polar

  • Reflected and intersecting shocks, Prandtl-Meyer expansion waves

  • Curved shocks

  • Nozzle and diffuser design

  • Reflection of waves from the free boundary

4. Linearized potential flow: 5 Lectures

  • Small-perturbation theories

  • Linearized velocity potential flow: Subsonic and supersonic flow

  • Thin airfoil and slender body

  • Numerical methodss

5. Compressible boundary layers: 6 Lectures

  • Governing equations for compressible flow

  • Compressible boundary layer

  • Viscous and compressibility effect

  • Similarity solution

  • Results of Cohen and Reshotko, Recovery factor

  • Shock wave-boundary layer interactions

6. Compressible turbulent flows: 5 Lectures

  • Mass-averaged Navier-Stokes Equationsw

  • Eddy-viscosity concept, Reynolds stresses, and heat flux tensor

  • Effect of compressibility and higher-order correlations

  • Difficulties in turbulent flow modeling because of temperature fluctuations

  • Experiments: Pressure probe, hotwire, and optical techniques

7. CFD: Time-marching technique for compressible flow: 5 Lectures

  • Introduction to the time-marching solution

  • The blunt body problem

  • Nozzle/diffuser flows

8. Hypersonic flow: 4 Lectures

  • Introduction

  • Hypersonic shock wave relation

  • Hypersonic small-disturbance equations

  • Hypersonic similarity

  • CFD applied to hypersonic flow

9. High-temperature flow (an additional topic to be covered if time permits): 4 Lectures

  • Thermodynamics and chemical reaction

  • Nonequilibrium Flows

  • Plasma formation, ionization and vibrational excitation

  • Nonequilibrium shock wave and nozzle flow

    Recommended books


      1. Modern Compressible Flow, 3rd edition, by John Anderson, Mc Graw Hill Publication (2003).

    Reference books

          1. Introduction to Compressible Fluid Flow, Second Edition, by Patrick H Oosthuizen and William E. Carscallen, CRC Press (2013).

          2. Compressible Fluid Dynamics, by P. A. Thompson, McGraw-Hill,New York, 1972.

          3. Elements of Gas Dynamics, By H. W., Liepmann, and A. Roshko, Dover Publications, Mineola, NY: 2001. Originally from Wiley, 1957.

          4. Viscous Fluid Flow, 2nd ed, by F. M. White, McGraw-Hill, New York, 1991.

          5. Compressible Fluid Flow, 2nd ed. by M. A. Saad, Prentice-Hall, 1993.

          6. Introduction to Physical Gas Dynamics, by W. G. Vincenti, and C. H. Kruger, Krieger, Melbourne, 1975.

    Proposing instructors: Dr. Subrata Sarkar