Unsteady oblique shock waves

Emanuel, George; Yi, T.H.

doi:10.1007/s001930050184

Cited by 7 publications

(3 citation statements)

References 2 publications

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“…Numerous studies have been performed on the stability of oblique shocks, 7−10 as well as their oscillations characteristics. 8,12 …”

Section: Application To Oblique Shock Wavesmentioning

confidence: 98%

“…3−6 The stability of the strong and weak solutions to supersonic flow over a wedge has been studied via perturbation analysis, 7−10 as well as methods of computationally treating oblique shock oscillation. 11,12 Finally, inlets of pulse detonation engines are prone to unsteady flows because of the periodic nature of the detonations. 13−16 A primary concern connected with shock motion in inlets is that it can lead to engine unstart, but in the present work it shall be shown that unsteadiness might have other consequences as well.…”

Section: Introductionmentioning

confidence: 99%

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Time-Averaged Entropy and Total Pressure Ratios Across Unsteady Inlet Shock Waves

Lewis

Smith

2005

Journal of Propulsion and Power

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Unsteady shock-wave motion can have a significant effect on the flow in a supersonic inlet, or in a compressor or turbine passage. One particular consequence of unsteadiness is that the time average of moving shock-wave properties can be noticeably different than the corresponding values for a steady shock. Of special interest to propulsion applications, shock unsteadiness can either increase or decrease the time-averaged total pressure ratio in the shock reference frame and the time average of frame-independent entropy jump, depending on the shocknormal Mach number. However, unsteadiness will always lead to a decrease in time-averaged total pressure ratio in the absolute frame and thus downstream of the unsteady shock. An analysis is presented, which includes time averaging of the sinusoidally perturbed, quasi-steady Rankine-Hugoniot equations, from which the time-dependent responses are calculated using both a differential and integral approach. Functions are derived that permit the direct calculation of time-averaged unsteady losses in total pressure and increase in entropy, assuming sinusoidal perturbation. Both computational and analytical studies have been performed to quantify the conditions under which the shock entropy jump will either increase or decrease as a result of periodic unsteadiness. Nomenclature M = Mach number P = pressure, Pa R = gas constant for air, 287 J/kg-K s = entropy, J/kg-K T = temperature, K β = shock-wave angle γ = ratio of specific heats = shock jump value ε = ratio of perturbed value to steady state θ = oblique surface angle µ = Mach number perturbation amplitude ρ = density, kg/m 3 φ = pressure perturbation amplitude Subscripts 0 = total conditions 1 = upstream value 2 = downstream value ∞ = freestream conditions

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“…Numerous studies have been performed on the stability of oblique shocks, 7−10 as well as their oscillations characteristics. 8,12 …”

Section: Application To Oblique Shock Wavesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Time-Averaged Entropy and Total Pressure Ratios Across Unsteady Inlet Shock Waves

Lewis

Smith

2005

Journal of Propulsion and Power

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“…In the following we need shock relations and flow quantities defined on the ground frame. Note that shock relations for moving oblique shock waves are provided by Emanuel & Yi (2000).…”

Section: Shock Relations For Steady and Moving Shock Wavesmentioning

confidence: 99%

Transition study for asymmetric reflection between moving incident shock waves

Wang

2021

J. Fluid Mech.

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The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.

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Unsteady shock generated vorticity

Emanuel

2000

Shock Waves

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Unsteady oblique shock waves

Cited by 7 publications

References 2 publications

Time-Averaged Entropy and Total Pressure Ratios Across Unsteady Inlet Shock Waves

Time-Averaged Entropy and Total Pressure Ratios Across Unsteady Inlet Shock Waves

Transition study for asymmetric reflection between moving incident shock waves

Unsteady shock generated vorticity

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