This course essentially deals with the very high speed fluid flows, mainly the flows in
the regime of supersonic speed. Hence understanding of this flow regime and its
characteristic signatures is the objective of this course.
Theoretical understanding of this
subject along with the experimental introduction is very useful for advanced studies
like missile and reentry aerodynamics and hypersonic aerothermodynamics. Hence, inorder
to build the basic platform, this course starts with basic governing equations of
the fluid flows.
Modifications of these equations for simplified studies of one
dimensional flow and certain special cases like Rayleigh flow and Fanno flow are
introduced afterwards. One more example of one dimensional flow as normal shock
wave follows the same chapter.
Concept of oblique shock as a consequence of two
dimensional flows along with various conditions is the part of next chapter. Expansion
of the supersonic flow and basic governing equations are also part of the two
Quasi-one dimensional flow and understanding of supersonic
nozzle and diffuser follows this. Unsteady flows and method of characteristics with itsapplication ends the theoretical understanding in the course. However this course ends
with the introduction to various experimental facilities of this flow regime.
Contents: Basic concepts of thermodynamics, governing equations in various forms,
concept of Mach number, one dimensional flows and normal shock wave, Reylaigh and
Fanno flows, Two dimensional flows and oblique shock waves, θ-B-M relations,
understanding of shock interaction and shock reflection with various graphs, Prandtl-
Mayer expansion, shock-expansion theory, quasi one dimensional flows, method of
characteristics and, unsteady wave motion and introduction to various experimental
facilities for these speed ranges.
Basic concepts : Introduction to compressible flow, A brief
review of thermodynamics and fluid mechanics, Integral forms
of conservation equations, Differential conservation equations,
Continuum Postulates, Acoustic speed and Mach number,
Governing equations for compressible flows.
One-dimensional compressible flow: One dimensional flow
concept, Isentropic flows, Stagnation/Total conditions,
Characteristics speeds of gas dynamics, Dynamic pressure and
pressure coefficients, Normal shock waves, Rankine-Hugonoit
equations, Rayleigh flow, Fanno flow, Crocco’s theorem.
Two-dimensional flows: Oblique shock wave and its governing
equations, θ-B-M relations, The Hodograph and Shock Polar,
Supersonic flow over wedges and cones, Mach line, Attached
and Detached shock, Reflections and interaction of oblique shock
waves, Expansion waves, Prandtl-Meyer flow and its governing
equations, Supersonic flow over convex and concave corners,
Approximation of continuous expansion waves by discrete
Quasi-one dimensional flows: Governing equations, Areavelocity
relations, Isentropic flow through variable-area ducts,
Convergent-divergent (or De Laval) nozzles, Over-expanded
and under-expanded nozzles, Diffusers.
Unsteady wave motions: Moving normal shock waves, Reflected
shock waves, Physical features of wave propagation, Elements of
acoustic theory, Incident and reflected waves, Shock tube
relations, Piston analogy, Incident and reflected expansion
waves, Finite compression waves, Shock tube relations.