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16.120

Compressible Internal Flow

3-0-9 units · Graduate

Internal compressible flow with applications in propulsion and fluid systems. Control volume analysis of compressible flow devices. Compressible channel flow and extensions, including effects of shock waves, momentum, energy and mass addition, swirl, and flow non-uniformity on Mach numbers, flow regimes, and choking.

Spring 2003 · Compressible Flow

Topics

  • Basics (3 Lectures by Prof. Zoltan Spakovszky)
  • Continuity and Momentum Equations (Seen Before so no Detailed Derivation) Derivation of Energy Equation for a Compressible, Viscous, Heat Conducting Fluid
  • Thermo - and Mechanical Processes, Splitting the Energy Equation Entropy Changes and Thermodynamic Context Physical Meaning of the Terms, 2nd Law Exact Solution of the Navier-Stokes Equations for a One-Dimensional Flow Physical Insight into Shock Thickness and the “Origin” of Losses for a Shock Wave
  • Integral Forms of Equations of Motion Non-dimensional Parameters Characterizing Compressible Flow “Appropriate” Scaling-what are the Relevant Nondimensional Parameters? When is a Flow Compressible [For Both Steady and Unsteady Flow]?
  • Quasi 1-D Compressible Flow and Extensions (8 Lectures by Prof. Zoltan Spakovszky)
  • Physical Basis for the 1-D Flow Assumption, Role of 1-D Flow Descriptions (Insight, Overall Flow Characterization), Regimes of Relevance 1-D Isentropic Flow and Choking, Maximum Flow Per Unit Area “Corrected Flow” and Flow Functions
  • 1-D Flow in Converging-diverging Nozzles Shock Waves, Behavior of Nozzles (Brief Description) Starting of Supersonic Flows Transitions from Supersonic to Subsonic Flow in Constant Area Ducts
  • Generalized One-dimensional Flow With Mass, Momentum, and Energy Interchange Effect of Friction (Movement of Choke Point, Reduction in Max Flow) Effect of Heat Addition Analogies Between Mass, Momentum, and Heat Addition
  • General Compressible Flow Processes in Propulsion Systems Representation of Flow Processes in H-K Diagrams Applications to Ramjets and Scramjets
  • Axisymmetric Compressible Swirling Flow Derivation of Equations Examples: (i) Behavior of Static Pressure, (ii) Effects of Swirl on Maximum Mass Flow, (iii) Effect of Mass Addition on Total Pressure
  • Compound-compressible Flow (Combined Subsonic and Supersonic Streams) Compound Flow Regimes and the Compound Mach Number Compound Choking and Effect on Mass Flow Examples: Nozzles, Mixing Ducts
  • Disturbance Behavior in a Compressible Flow (2 Lectures by Prof. Zoltan Spakovszky)
  • Types of Perturbations in Compressible Flow: Entropy, Vorticity and Pressure Disturbances Coupling of Disturbance Types in Compressible Flow
  • Characteristic Disturbance Velocities and Behavior Unsteady Flow and Upstream Influence in Compressible Flow
  • Gas Dynamic Discontinuities (4 Lectures by Prof. Wesley Harris)
  • Shock Waves
  • Deflagrations
  • Detonations
  • Crocco’s Theorem
  • Two-Dimensional, Compressible, Linear Flows (4 Lectures by Prof. Wesley Harris)
  • Constant Entropy Flows
  • Slender, Axially Symmetric Flows
  • Two-Dimensional, Compressible, Non-Linear Flows (4 Lectures by Prof. Wesley Harris)
  • Inviscid, Unsteady Transonic Flows
  • Inviscid Hypersonic Flows

Readings

  • Anderson, J. D. Modern Compressible Flow with Historical Perspective. McGraw-Hill Publishers, 1990.
    Listed reading
  • Emmons, H. W. Fundamentals of Gas Dynamics , Chapter 1, “The Equations of Gas Dynamics”, by H. S. Tsien, Volume III in the Princeton Series of Volumes on “High Speed Aerodynamics and Jet Propulsion”, Princeton University Press, 1958 (Be warned: there is a mistake in the derivation of the energy equation in differential form!)
    Listed reading
  • Liepmann, H., and A. Roshko. Elements of Gas Dynamics. John Wiley Publishers, 1957 (see chapters 7 and 13).
    Listed reading
  • Schlichting, H. Boundary Layer Theory. 7th ed. McGraw-Hill Publishers, 1979. Chapter 3.
    Listed reading
  • Thompson, P. A. Compressible Fluid Dynamics. Maple Press Company, 1984.
    Listed reading
  • White, F. M. Viscous Fluid Flow. 2nd ed. McGraw-Hill Publishers, 1991. Chapter 2.
    Listed reading
  • Greitzer, E.M., Tan, C.S, Graf, M.B. and J.E. Ffowcs Williams (Ed.). Internal Flow: Concepts and applications . Cambridge University Press, 2004. Chapter 1.
    Listed reading
  • Anderson, L. R., W. H. Heiser, and J. C. Jackson. “Axisymmetric One-Dimensional Compressible Flow—Theory and Applications.” ASME Transactions, Journal of Applied Mechanics (1970): pp. 917-923.
    Listed reading
  • Bernstein, A., W. H. Heiser, and C. Hevenor. “Compound-Compressible Nozzle Flow.” AS_ME Transactions, Journal of Applied Mechanics_ (1967): 548-554.
    Listed reading
  • Emmons, H. W. Fundamentals of Gas Dynamics , Chapter 2, “The Equations of Gas Dynamics,” by L. Crocco, Volume III in the Princeton Series of Volumes on “High Speed Aerodynamics and Jet Propulsion”. Princeton University Press, 1958.
    Listed reading
  • Heiser, W. H., and D. T. Pratt. Hypersonic Airbreathing Propulsion. AIAA Education Series, 1994. Chapter 2.
    Listed reading
  • Hill, P., and C. Peterson. Mechanics and Thermodynamics of Propulsion. Addison Wesley Publishers, 1992. Chapter 3.
    Listed reading
  • Li, W.-H., and S. -H. Lam. Principles of Fluid Mechanics. Addison-Wesley Publishing Company, 1964. Chapters 14 and 15.
    Listed reading
  • Shapiro, A. H. The Dynamics and Thermodynamics of Compressible Fluid Flow. Vol. 1. Ronald Press. Chapters 1 to 8.
    Listed reading
  • Tew, D. E., B. S. Teeple, and I. A. Waitz. “Mixer-Ejector Noise Suppressor Model.” J. Propulsion and Power 14. No. 6 (1998): 941-950. (This shows a recent application and extension of the compound compressible flow ideas in reference 2)
    Listed reading
  • Greitzer, E.M., Tan, C.S, Graf, M.B. and J.E. Ffowcs Williams (Ed.). Internal Flow: Concepts and applications . Cambridge University Press, 2004. Chapters 2, 10, 11.
    Listed reading
  • Dowling, A. P., and J. E. Ffowcs Williams. Sound and Sources of Sound. Ellis Horwood Press, 1983.
    Listed reading
  • Lighthill, J. Waves in Fluids. Cambridge University Press, 1978.
    Listed reading
  • Morse, P. M., and Ingard. Theoretical Acoustics. Princeton University Press, 1986.
    Listed reading
  • Greitzer, E.M., Tan, C.S, Graf, M.B. and J.E. Ffowcs Williams (Ed.). Internal Flow: Concepts and applications . Cambridge University Press, 2004. Chapter 6.
    Listed reading
  • Hayes, W. D. Gasdynamic Discontinuities. No. 3. Princeton Aeronautical Paperbacks. Princeton, NJ: Princeton University Press, 1960.
    Listed reading
  • Ashley, H., and M. Landahl. Aerodynamics of Wings and Bodies. Reading MA: Addison-Wesley Publishing Co., Inc., 1965.
    Listed reading
  • Katz, J. and A. Plotkin. Low-Speed Aerodynamics: From Wing Theory to Panel Methods. New York, NY: McGraw-Hill, Inc., 1991.
    Listed reading
  • Landahl, M. T. Unsteady Transonic Flow. New York, NY: Pergamon Press, 1961.
    Listed reading
  • Chernyi, G. G. Introduction to Hypersonic Flow. New York, NY: Academic Press, 1961.
    Listed reading

Prerequisites & course information

Prereq: 2.25 or permission of instructor Acad Year 2027-2028: Not offered Acad Year 2028-2029: G (Spring) 3-0-9 units

Sources