Self-Similar Solutions for the Triple Point Paradox in Gasdynamics

Tesdall, Allen M.; Sanders, Richard; Keyfitz, Barbara Lee

doi:10.1137/070698567

Cited by 55 publications

(42 citation statements)

References 16 publications

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“…The ratio between the supersonic patch size and the virtual Mach stem was found to be in the range of 2.3-4.8%. This compared reasonable well with the 2% obtained experimentally in [11], but the experimental results are large when compared to numerical work in [12] where a value of 0.6% was obtained. This consistently obtained increase in length will be the a b Fig.…”

Section: Evidence Of Shockletssupporting

confidence: 77%

“…According to Tesdall et al [9], an infinite sequence of expansion waves and shocklets beneath the reflected wave are predicted for an inviscid flow. However, since the waves in this study are very weak and viscous effects are present, it is not surprising that the sequence of supersonic patches as observed in [9,12] is not detected. The triple point also undergoes a number of reflections (2)(3)(4)(5) off the ceiling and the floor of the shock tube, which could possibly dampen and degrade the integrity of the flow features behind the triple point since the reflected wave impinges on the boundary layer induced behind the incident wave.…”

Section: The Expansion Wavementioning

confidence: 89%

“…Figure 11 is a plot of the size of the supersonic patch, l s , versus the virtual Mach stem length, l vms , for M ≈ 1.20. It is expected, from the numerical work in [9,12], that the size of the supersonic patch is directly proportional to the virtual Mach stem length. When comparing similar data sets shown in Fig.…”

Section: Evidence Of Shockletsmentioning

confidence: 99%

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Guderley reflection for higher Mach numbers in a standard shock tube

Cachucho

Skews

2011

Shock Waves

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An experimental study shows that the Guderley reflection (GR) of shock waves can be produced in a standard shock tube. A new technique was utilised which comprises triple point of a developed weak Mach reflection undergoing a number of reflections off the ceiling and floor of the shock tube before arriving at the test section. Both simple perturbation sources and diverging ramps were used to generate a transverse wave in the tube which then becomes the weak reflected wave of the reflection pattern. Tests were conducted for three ramp angles (10 • , 15 • , and 20 • ) and two perturbation sources for a range of Mach numbers (1.10-1.40) and two shock tube expansion chamber lengths (2.0 and 4.0 m). It was found that the length of the Mach stem of the reflection pattern is the overall vertical distance traveled by the triple point. Images with equivalent Mach stem lengths in the order of 2.0 m were produced. All tests showed evidence of the fourth wave of the GR, namely the expansion wave behind the reflected shock wave. A shocklet terminating the expansion wave was also identified in a few cases mainly for incident wave Mach numbers of approximately 1.20.

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Section: Evidence Of Shockletssupporting

confidence: 77%

Section: The Expansion Wavementioning

confidence: 89%

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Guderley reflection for higher Mach numbers in a standard shock tube

Cachucho

Skews

2011

Shock Waves

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“…To simplify the notations, we let F = F − U and G = G− U, and the problem in conserved form (5) can be rewritten as [4,15] U +F +G +2U = 0.…”

Section: The Numerical Methodsmentioning

confidence: 99%

Numerical solutions to the self-similar transonic two-dimensional nonlinear wave system

Kim

Lee

2010

Math. Meth. Appl. Sci.

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We present numerical results on a two-dimensional Riemann problem governed by the self-similar nonlinear wave system that gives rise to a transonic shock. We consider a configuration for a vertical incident shock moving to the right above a rectangular object. The incident shock then interacts with a sonic circle soon after it moves beyond the object, and creates a transonic region. We implement Lax-Liu positive schemes and Strang splitting, and obtain several numerical solutions for the model system. With the numerical results that we have obtained, we present several analyses of the transonic shock strengths and the positions of the transonic shocks with various Riemann data. Moreover, due to the presence of the corner of the object, numerical oscillations are apparent. We discuss regularity results for the solution near the corner of the object.

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“…This brings up Euler system's von Neumann triple point paradox, for which John Hunter and collaborators have produced numerical evidence of Guderley reflection [10,35,36]. See Skews and Ashworth [30] for physical experimental evidence.…”

Section: Initial Datamentioning

confidence: 99%

Two-dimensional Riemann problems for the compressible Euler system

Zheng

2009

Chin. Ann. Math. Ser. B

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Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult, but a viable alternative remains missing. We list merits of one-dimensional Riemann problems and compare them with those for the current two-dimensional Riemann problems, to illustrate their worthiness. We approach twodimensional Riemann problems via the methodology promoted by Andy Majda in the spirits of modern applied mathematics; that is, simplified model building via asymptotic analysis, numerical simulation, and theoretical analysis. We derive a simplified model, called the pressure gradient system, from the full Euler system via an asymptotic process. We use state-of-the-art numerical methods in numerical simulations to discern small-scale structures of the solutions, e.g., semi-hyperbolic patches. We use analytical methods to establish the validity of the structure revealed in the numerical simulation. The entire process, used in many of Majda's programs, is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws. SystemsWe consider the two-dimensional (2-D) compressible Euler systemwhere ρ is density, u is velocity vector, p is pressure, E = |u| 2 /2 + γp/ρ is the total energy density, and γ > 1 is the gas constant. We also consider the so-called pressure gradient system

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Self-Similar Solutions for the Triple Point Paradox in Gasdynamics

Cited by 55 publications

References 16 publications

Guderley reflection for higher Mach numbers in a standard shock tube

Guderley reflection for higher Mach numbers in a standard shock tube

Numerical solutions to the self-similar transonic two-dimensional nonlinear wave system

Two-dimensional Riemann problems for the compressible Euler system

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