Waves and compressible flow

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This version of the course was held for the last time Spring The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian. University of Oslo P. Box Blindern Oslo. Main navigation jump Main content jump Theme navigation jump Contact information jump. For employees Norwegian website.

Search our webpages Search. Menu Search. This course is discontinued. Course content Sound waves, discontinuities, shock waves, subsonic, transsonic and supersonic flow, flow in pipes at large velocities, one-dimensional flow, hydraulic jump analogy, stationary shock waves, normal and skew shock, Prandtl-Meyer expansion. Learning outcome To provide an introduction to compressible flow and can be used for a master study in fluid mechanics or branches of physics or astrophysics.

Admission Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

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Overlapping courses 9 credits with ME However all we are really seeing is a region of space where large changes are occurring. As it flies along it produces noise, noise from its engines, noise from its passage through the air and possibly even a crying baby or two. The sound waves associated with this noise propagate outwards in all directions, at the speed of sound.

If the plane is travelling with reasonable speed but still subsonic , you can imagine that the waves in front might bunch up a little compared with the waves behind it. This is the well-known doppler effect you can hear this easily when a vehicle with a siren drives past. Now let us imagine that the plane accelerates up to the speed of sound.

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This book aims to give readers a broad mathematical basis for modeling and understanding the wide range of wave phenomena encountered in modern. Now in its second edition, this book continues to give readers a broad mathematical basis for modelling and understanding the wide range of wave phenomena.

All the acoustic energy associated with those sound waves will now reach us at the same time, rather than being spread out. When we compress a whole lot of sound waves together into a single wave, what we have is now essentially a shock wave. If the plane accelerates to speeds higher than the speed of sound, it will now start outrunning its own sound waves! This will form a shock wave in a cone behind the aircraft.

velocity of sound wave in a compressible fluid

The more supersonic the aircraft is, the further past us it will be before we hear it, and the louder it will be when we do! This is one way to visualize how a shock wave forms — acoustic waves cannot propagate faster than the speed of sound, so you get a build-up of waves in one place, resulting in a shock wave.

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This gives the air time to adjust and flow smoothly over the aircraft. The flow is divided into 3 distinct regions.

Turbulence and acoustic waves in compressible flows

The solution to determine the properties of these regions is to recognize that the flow in region 2 must turn parallel to the compression surface. Since mdot is constant, this means that the inviscid cross-sectional area must decrease along the flow path.

Course content

Chapter 3 J. They will have an awareness of shock waves and how the theory of characteristics for PDEs can be applied to study those associated with supersonic flight. The applets are slowly being updated, but it is a lengthy process. One suggestion is to provide more illustrations in the other chapters, to convey a similar wealth of physical insight to the student. This volume is mainly devoted to inviscid flows. Nov , 57 6 : B When the flow deflection angle is increased above a certain angle, there is no solution.

However, because real flows are viscous, with boundary layers, the actual cross-sectional area along the flow path will be varied to achieve the purposes of the design: some other stuff. In example 4. The second case achieves the same Mach number change 2.

Turbulence and acoustic waves in compressible flows

The multiple shock system caused much less total pressure loss than the single oblique shock. This is a general result: a supersonic flow can be decelerated and compressed much more efficiently by a system of multiple oblique shocks than by a single stronger shock. High-speed aircraft inlets and supersonic wind tunnels use this principle to slow down and pressurize supersonic flow. Consider the intersection of left-running and right-running oblique shocks as shown in Figure 4.

A is a left-running wave and B is a right-running wave.

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A and B continue as refracted shocks C and D downstream of their intersection E. So, the entropy in region 4' is greater than that in region 4; thus the entropy is discontinuous acroos the "slip line.

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Consider two left-running oblique shock waves generated by two compression corners, as described in Figure 4. Shock waves AC and BC will intersect. Above the point C intersection point , a single shock wave CD will propagate.

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