Oblique shock waves heres a quick refresher on oblique shock waves. An airplane that is designed to fly supersonic will have very sharp edged surfaces, in order to have the least amount of drag. It is claimed that an oblique shock can be analyzed like a normal shock provided that the normal component of velocity normal to the shock surface is used in the analysis. They emanate from the wings of a supersonic aircraft, from a large explosion, from a jet engine, and ahead of the projectile in a gun barrel. A second series shows the effects of caloric imperfections on continuous onedimensional flow and on the flow through normal and oblique shock waves. The line is colored blue for an oblique shock and magenta when the shock is a normal shock.
Refraction of a normal shock wave at headon incidence. Aspects of planar, oblique and interacting shock waves in an. Continuum shock wave structure condensation discontinuities unsteady 1d flows. Introduction the practical analysis of compressible flow involves frequent application of a few basic results.
Oblique shock waves will then be discussed in the next chapter. Notice that downstream to the right of the shock wave, the lines are closer together than upstream. Unlike after a normal shock where m 2 must always be less than 1, in oblique shock m 2 can be supersonic weak shock wave or subsonic strong shock wave. Noraml and oblique shock waves aiaa education series. First, we will consider the normal shock wave, as shown in fig. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium. Find, read and cite all the research you need on researchgate. Shock waves represent an extremely important physical phenomena which appears to be of special practical importance in three major fields. A shock wave will make an oblique angle with respect to the upstream flow is called oblique shock wave. M 1n oblique shock can thus be analyzed as a normal shock with m 1 and m 2 replaced by m andm u 1n u 1 sin.
Shock waves in general very strong, extremely thin, waves propagating supersonically, producing almost instantaneous deceleration, compression, increase in pressure, density and temperature, of the flow normal shocks perpendicular to the flow always decelerate flow to subsonic speed. School of aerospace engineering supersonic flow turning. Figures 8 to 11 shows the results of the supersonic cascade calculation. Finite amplitude waves, characteristics, riemann invariants. The result shows good agreement when compared with analytical solution. The normal shock waves of real gases and the generalized. The weak and strong oblique shock waves appeared iopscience. They described two types of shock wave reflection from the inclined surface figure 1. The shock wave angle can be calculated by the implicit oblique shock wave theory e. A shock wave obeys the usual laws of fluid mechanics. Depending on the shape of the object and the speed of the flow, the shock wave may be inclined to the flow. The black lines show the streamlines of the flow past the wedge. Significance of compressible flows isentropic flow a. The conditions under which the strong and weak oblique shock waves are generated were not discussed in these studies, thereby.
The shock relations are best analysed in the frame of the shock in which its velocity is zero. The handbook of shock waves contains a comprehensive, structured coverage of research topics related to shock wave phenomena including shock waves in gases, liquids, solids, and space. Equations, tables and charts for compressible flow nasa. This indicates an increase in the density of the flow. Approximate formula of weak oblique shock wave angle. Further reductions in back pressure cause the angle between the shock and the flow to. Pdf approximate formula of weak oblique shock wave angle.
Computation of thermally perfect properties of oblique shock waves. If the shock wave thickness length scale is too small to be of signi. Normal shock waves obey conservation of mass, momentum, and energy, and the 2nd law of thermodynamics. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. Weak solutions are often observed in flow geometries open to atmosphere such as on the outside of a.
The theoretical prediction of oblique shock relation was chosen as following. Oblique shock analysis dictates that only the normal velocity component u can change across any wave, so that dv must be entirely due to the normal velocity change du. An oblique shock wave is a shock wave that, unlike a normal shock, is inclined with respect to the incident upstream flow direction. The tables present useful dimensionless ratios for continuous onedimensional flow and for normal shock waves as functions of mach number for air considered as a perfect gas.
Queens university mech 448 chapter fivechapter five. At say time r0, the incident wave i is generated by a suitable boundary disturbance such as a driving or withdrawing piston. The upstream streamlines are uniformly deflected after the shock wave. Normal shock tables university of california, berkeley. In physics, a shock wave also spelled shockwave, or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Normal shock wave oblique shock wave rarefaction waves viscous and thermal boundary layers farfield acoustic wave figure 1. These oblique shock waves provide the mechanism by which the pressure increases to that downstream of this adjustment process. The oblique shock relations can be deduced from normal shock relations by noting that the oblique can produce no momentum change parallel to the. Shock waves are largeamplitude waves that travel in a gas.
General laws for propagation of shock waves through matter 3. The program can also calculate oblique shock waves generated by a sequence of compression ramps such as in scramjet intakes, for instance, by yielding. The linear stability of oblique shock waves has been studied in, the author s5tudied the stability with respect to small perturbation in the incoming ow and in the solid surface. A wedge cascade with oblique shock waves was simulated. Computation of thermally perfect properties of oblique shock waves atomic, polyatomic, or any specified mixture thereof. Incipient separation in shock wave boundary layer interactions as induced by sharp fin 22 july 2006 shock waves, vol.
The process of oblique shock is adiabatic and irreversible i. Piston problems, boundary interactions, shock tubes. For the first time the problem of shock wave reflection for the nonstationary case was considered in e. Me 6604 gas dynamics and jet propulsion unit iii shock waves mrs. Spc 407 sheet 4 compressible flow oblique shock wave. It is valid for all materials and guarantees the existence of at least one solution to the hugoniot equation. Pdf a computer program for calculating normal and oblique shock. The code serves the function of the tables and charts ofnaca rep. The oblique shock wave produced by a three dimensional wing has been analyzed in 2 3 4. There are equations which describe the change in the flow variables. This work presents the modeling and validation results of a newly developed computer program for calculating airflow conditions behind normal and oblique shock waves considering two distinct gas models for the air. Chapter elevennormal shock in converging diverging. The left of the shock wave we hav e the initial conditions and. These shock waves are known as oblique shock waves.
Chapter general laws for propagation of shock waves. If the shock wave is perpendicular to the flow direction, it is called a normal shock. Computation of thermally perfect properties of oblique. Oblique shock project gutenberg selfpublishing ebooks. Lecture notes compressible fluid dynamics mechanical. When this shock wave is perpendicular to the direction of the onedimensional flow, a normal shock wave transforms the flow to a subsonic one. The general situation depicted above is an oblique shock.
Shock doesnt change velocity component n u 2 u 1 u 1t u 2 tangent to it, so u t1 u t2 u t observer traveling along shockat u seesanormal u 1. The equations are derived from the conservation of mass, momentum, and energy. For normal shocks, flow is perpendicular to shock no change in flow direction how does supersonic flow change direction, i. By this i mean to say that when we analyze the control volume shown in figure 3, energy inenergy out. Shock waves occur supersonic flows where the flow velocity exceeds the adiabatic. American institute of aeronautics and astronautics 12700 sunrise valley drive, suite 200 reston, va 201915807 703. Further reductions in back pressure cause the angle between the shock and the flow to decrease, thus.
In this video, we will be using four different ways of solving a simple normal shock problem. This shock wave, weaker than a normal shock, is called an oblique shock. Curved shock waves are relatively difficult to analyze and they will not be discussed in detail in the present course. Normal shock wave parameters 14 tables 15 graphs 15 comparison of the results with other solutions 16 application to oblique shock waves 18 summary 19 references 21 appendix 24 table i atmospheric properties as a function of altitude 26 table ii normal shock wave parameters 27. Normal shock waves occur, for example, in the intakes.
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