LECTURENOTESON GASDYNAMICS - University of …

1 LECTURE NOTES ONGAS DYNAMICSJ oseph M. PowersDepartment of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre Dame, Indiana 46556-5637 USAupdated28 October 2019, 7:15pm2CC BY-NC-ND. 28 October 2019, J. M. Definitions .. Motivating examples .. Re-entry flows .. Bow shock wave .. Rarefaction (expansion) wave .. Momentum boundary layer .. Thermal boundary layer .. Vibrational relaxation effects .. Dissociation effects .. Rocket nozzle flows .. Jet engine inlets .. 132 Governing Mathematical preliminaries .. Vectors and tensors .. Gradient, divergence, and material derivatives .. Conservative and non-conservative forms.

2 Conservative form .. Non-conservative form .. Summary of full set of compressible viscous equations .. Conservation axioms .. Conservation of mass .. Nonconservative form .. Conservative form .. Incompressible form .. Conservation of linear momenta .. Nonconservative form .. Conservative form .. Conservation of energy .. Nonconservative form .. Mechanical energy .. Conservative form .. Energy equation in terms of entropy .. Entropy inequality .. Constitutive relations .. Stress-strain rate relationship for Newtonian fluids .. Fourier s law for heat conduction .. Variable first coefficient of viscosity.

3 Typical values of for air and water .. Common models for .. Variable second coefficient of viscosity, .. Variable thermal conductivity,k.. Typical values ofkfor air and water .. Common models fork.. Thermal equation of state .. Description .. Typical models .. Caloric equation of state .. Description .. Typical models .. Special cases of governing equations .. One-dimensional equations .. Euler equations .. Incompressible Navier-Stokes equations .. 383 Thermodynamics Preliminary mathematical concepts .. Summary of thermodynamic concepts .. Maxwell relations and secondary properties .. Internal energy from thermal equation of state.

4 Sound speed from thermal equation of state .. Canonical equations of state .. Isentropic relations .. 554 One-dimensional compressible Generalized one-dimensional equations .. Mass .. Momentum .. Energy .. Influence coefficients .. Flow with area change .. 73CC BY-NC-ND. 28 October 2019, J. M. Isentropic Mach number relations .. Sonic properties .. Effect of area change .. Choking .. Normal shock waves .. Governing equations .. Rayleigh line .. Hugoniot curve .. Solution procedure for general equations of state .. Calorically perfect ideal gas solutions .. Acoustic limit .. Non-ideal gas solutions.

5 Flow with area change and normal shocks .. Converging nozzle .. Converging-diverging nozzle .. Flow with friction Fanno flow .. Flow with heat transfer Rayleigh flow .. Numerical solution of the shock tube problem .. One-step techniques .. Lax-Friedrichs technique .. Lax-Wendroff technique .. 1235 Steady supersonic two-dimensional Two-dimensional equations .. Conservative form .. Non-conservative form .. Mach waves .. Oblique shock waves .. Small disturbance theory .. Centered Prandtl-Meyer rarefaction .. Wave interactions and reflections .. Oblique shock reflected from a wall .. Oblique shock intersection .. Shock strengthening.

6 Shock weakening .. Supersonic flow over airfoils .. Flat plate at angle of attack .. Diamond-shaped airfoil .. General curved airfoil .. Transonic transition .. 153CC BY-NC-ND. 28 October 2019, J. M. Linear flow Formulation .. Subsonic flow .. Prandtl-Glauret rule .. Flow over wavy wall .. Supersonic flow .. D Alembert s solution .. Flow over wavy wall .. 1567 Viscous Governing equations .. Couette flow .. Suddenly accelerated flat plate .. Formulation .. Velocity profile .. Starting transient for plane Couette flow .. Blasius boundary layer .. Formulation .. Wall shear stress .. 1638 Formulation.

7 Planar waves .. Spherical waves .. 166CC BY-NC-ND. 28 October 2019, J. M. are a set of class notes for a gas dynamics /viscous flow course taught to juniors inAerospace Engineering at the University of Notre Dame during the mid 1990s. The coursebuilds upon foundations laid in an earlier course where the emphasis was on subsonic idealflows. Consequently, it is expected that the student has some familiarity with many conceptssuch as material derivatives, control volume analysis, derivation of governing equations,etc. Additionally, first courses in thermodynamics and differential equations are probablynecessary. Even a casual reader will find gaps, errors, and inconsistencies. The authorwelcomes comments and corrections.

8 It is also noted that these notes have been influencedby a variety of standard references, which are sporadically and incompletely noted in thetext. Some of the key references which were important in the development of these notesare the texts of Shapiro, Liepmann and Roshko, Anderson, Courant and Friedrichs, Hughesand Brighton, White, Sonntag and Van Wylen, and Zucrow and this stage, if anyone outside Notre Dame finds these useful, they are free to makecopies. Full information on the course is found M. powersNotre Dame, Indiana; USACC BY: $\ = 28 October 2019 The content of this book is licensed under Creative Commons Attribution-Noncommercial-No Derivative Works BY-NC-ND. 28 October 2019, J.

9 M. 1 IntroductionSuggested Reading:Anderson, Chapter 1: pp. DefinitionsThe topic of this course is the aerodynamics of compressible and viscous does aerodynamics rest in the taxonomy of mechanics ?Aerodynamics a branch of dynamics that deals with the motion ofairand othergaseous fluids and with theforcesacting on bodies in motion relative to such fluids ( )We can say thataerodynamicsis a subset of ( ) fluid dynamicssince air is but one type of fluid, fluid mechanicssince dynamics is part of mechanics , mechanicssince fluid mechanics is one class of a branch of physical science that deals with forces and the motionof bodiestraditionally broken into: kinematics study of motion without regard to causality dynamics (kinetics) study of forces which give rise to motionExamples of other subsets of mechanics :910 CHAPTER 1.

10 INTRODUCTION solid mechanics quantum mechanics celestial mechanics relativistic mechanics quantum-electrodynamics (QED) magneto-hydrodynamics (MHD)Recall the definition of a fluid:Fluid a material which moves when a shear force is that solids can, after a small displacement, relax to an equilibrium configurationwhen a shear force is also that bothliquidsandgasesare fluidsThe motion of both liquids and gases can be affected by compressibilityand shear shear forces are important for both types of fluids, the influence of compressibility ingases is generally more thrust of this class will be to understand how to model the effects of compressibilityand shear forces and how this impacts the design of aerospace Motivating examplesThe following two examples serve to illustrate why knowledge of compressibility and sheareffects is Re-entry flowsA range of phenomena are present in the re-entry of a vehicle into the atmosphere.