Course
Gas Dynamics
Introductory concepts of compressible flow, Isentropic one-dimensional flow, Normal shocks – stationary and moving , applications, applications to supersonic wind tunnels, Shock tubes, Supersonic Pitot’ probes, oblique shock, reflection, Prandtl – Meyer expansion flow. Fanno flow & Rayleigh flow. Under and over expanded nozzles, Shock expansion method for flow over airfoils. Brief introduction to the methods of characteristics, Prandtl-Glauert and Goethert rules. Ackeret’s supersonic airfoil theory. Small perturbation equations for subsonic, transonic, supersonic and Hypersonic flow. Experimental characteristics of airfoils in compressible flow
Course structure & Assessments
4 credit course, weekly online assignments, 2 in-person invigilated quizzes, 1 in-person invigilated end term exam. For details, visit Academics.
| Week 1 | Review of basic concepts: Rotation and dilatation, compressibility in kinematic terms, review of thermodynamics, speed of sound, Equations of conservation of mass and momentum |
| Week 2 | Energy equation, Stagnation state, Bulk modulus and compressibility, Mach number, Non-dimensionalization of equations of fluid motion, Mach number similarity |
| Week 3 | Classification of flow regimes, Isentropy and iso-enthalpy, steady isentropic flow relations and reference conditions (stagnation and sonic) |
| Week 4 | Steady one-dimensional flows: Isentropic quasi-1-D flows, area relation, effect of pressure ratio, choking |
| Week 5 | Shock waves: Shock formation, scales for shock thickness and dissipation; Steady one-dimensional flows (cont): Normal shock relations, Thermodynamics of shock waves, Rayleigh line, Ranking-Hugoniot curve and jump conditions |
| Week 6 | Steady one-dimensional flows (cont): Weak shock relations, shock waves in quasi-1-D flow (convergent-divergent nozzle), supersonic wind tunnel, start/unstart of supersonic wind tunnel; 1-D flow with friction (Fanon flow), Fanon line |
| Week 7 | Steady one-dimensional flows (cont): Fanno flow (cont) and Rayleigh flow, choking due to friction and heating |
| Week 8 | 2-D steady supersonic flows: Oblique waves, Oblique shock relations, overexpanded jets, bow shock, Crocco’s theorem, pitot tube, regular reflection of shock waves, pressure-deflection diagram, slip line |
| Week 9 | 2-D steady supersonic flows (cont): Classification of shock wave reflection, Prantl-Meyer Expansion, underexpanded jets, reflection of shock and expansion at free shear layer; 2-D steady aerodynamics: shock expansion theory |
| Week 10 | 2-D steady aerodynamics (cont): Compressible potential equations, linearisation of potential equation, linearised subsonic flow, Prandtl-Glauert and Goethert rules, linearised supersonic flow, d’Alemberts solution and method of characteristics (MoC) |
| Week 11 | 2-D steady aerodynamics (cont): Transonic and hypersonic small perturbation potential equations and similarity, introductory ideas on MoC based nozzle design; 1-D unsteady flow: Moving shock and expansion fan, shock tube and shock tunnel. |
| Week 12 | Review |
Prescribed Books
The following are the suggested books:
H. Shapiro, Dynamics and Thermodynamics of Compressible Fluid Flow (Volume 1), John Wiley & Sons