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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
When the flow velocity exceeds the speed of sound (M>1), adjustments in the flow often take place through abrupt discontinuous surfaces called shock waves. This is one of the most interesting and unique phenomena that occurs in supersonic flow. A shock wave can be considered as a discontinuity in the properties of the flowfield. The process is irreversible. A shock wave is extremely thin, usually only a few molecular mean free paths thick (for air ≈10-5cm). A shock wave is, in general, curved. However, many shock waves that occur in practical situations are straight, being either at right angles to the flow path (termed a normal shock) or at an angle to the flow path (termed an oblique shock). In case of a normal shock, the velocities both ahead (i.e., upstream) of the shock and after (i.e., downstream) the shock are at right angles to the shock wave. However, in the case of an oblique shock there is a change in the flow direction across the shock.
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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[fluid dynamics] A shock wave propagation traveling with inclination with respect to the incident upstream flow direction, unlike a normal shock. An oblique shock wave is generally formed at the tip (wedge) of an object in supersonic, compressible, flow. An example is the thermodynamic discontinuity at the nose of a plane approaching, and subsequently exceeding Mach velocity. The wave is at this point deflected at an corner angle (θ), diverting with respect to the streamlines:α, the oblique shock angle, conforming to: tan θ = 2cot α[(M12sin2α − 1)/M12(γhc + cos 2α + 2)], where M1 represents the Mach number, and γhc the heat capacity ratio. The Mach wave itself is only an infinitesimally weak shock wave. The coalescing of a multitude of Mach waves originates an actual oblique shock wave, similar to the normal shock wave. The flow direction of the oblique shock wave is tangential to the surface of the disturbance. Similar principles also apply to nozzle flow (see Figure O.5).
Fundamentals of Fluid Mechanics
Published in Ethirajan Rathakrishnan, Instrumentation, Measurements, and Experiments in Fluids, 2016
The shock may be described as a compression front, in a supersonic flow field, across which the flow properties jump. The thickness of the shock is comparable to the mean free path of the gas molecules in the flow field. When the shock is normal to the flow direction it is called normal shock, and when it is inclined at an angle to the flow it is termed oblique shock. For a perfect gas, it is known that all the flow property ratios across a normal shock are unique functions of specific heats ratio, γ, and the upstream Mach number, M1.
Numerical investigation of the wet steam condensation flow characteristics in stator cascade with blade surface heating
Published in Engineering Applications of Computational Fluid Mechanics, 2020
Xu Han, Yunyun Yuan, Zeren Zhao, Yaonan Wang, Wei Zeng, Zhonghe Han
The distributions of the Mach number, supercooling and shock wave in each case are exhibited in Figure 4. With increasing heating intensity, a remarkable change in the Mach number occurs only on the blade surface and near the trailing edge, as shown in Figure 4(a). The Mach number at the throat is about 1.1 and at the outlet is about 1.2. The Mach number distribution is very similar under different conditions. Because the steam condenses in a very short time, the steam flow is reduced. The latent heat of condensation will heats the main steam flow, which resulting in the decrease of velocity and the sudden increase of pressure. Combined with Figure 4(b), the supercooling at the throat reaches the maximum value, and then the spontaneous condensation process occurs rapidly. The steam transits from non-equilibrium state to equilibrium state rapidly, and the supercooling at the downstream of the throat decreases rapidly. The pressure increases after the oblique shock wave. At the cascade outlet, with an increase in heating intensity, the gradient of the Mach number and supercooling at the cascade throat decrease, with a decline in the strength of the condensation shock wave. When it reaches 700 kW/m2, the red region is divided. This division is because when the heat flux is too large, the superheated steam area in the blade wake is extremely expanded, and the heat cannot be transmitted in time, resulting in steam blockage and new shock waves, as shown in Figure 4(c).
Simulation of the effects of dilution gas for the formation of CJ plane during the oblique detonation
Published in Numerical Heat Transfer, Part A: Applications, 2023
The inlet temperature, pressure, and Mach number were 300 (K), 101.3 (kPa), and 8.0. The oblique detonation waves were induced by wedge angles (23 degrees). A supersonic gas encountering a wedge generates an oblique shock. As soon as the temperature and pressure increase caused by the shock is high enough, chemical reactions begin behind the shock [6]. The boundary conditions were same as Li et al. [6].