Measurement of Shock Wave Thickness by the Electron Beam Fluorescence Method

Robben, F.

doi:10.1063/1.1761728

Cited by 116 publications

(41 citation statements)

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“…[1][2][3][4][5] The reciprocal shock thickness in helium agrees reasonably well with the results of bimodal calculations 9 and with the few available experimental data.…”

Section: Salvador Monterosupporting

confidence: 75%

“…A discussion of these aspects has been given by Kogan, 1 Cercignani, 2 and others. [3][4][5] Moreover, due to the sparse experimental temperature and velocity data on welldefined 1D shock waves produced in shock tubes, little was known about the actual merits of NS equations to model the profiles of these quantities across the shock wave. This limitation has prevailed up to now in spite of the wealth of density and temperature data on 2D shock waves produced in jets.…”

Section: Salvador Monteromentioning

confidence: 99%

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Numerical simulation of shock-wave structure for argon and helium

2005

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We compare the thickness of shock-wave fronts at different Mach numbers, modeled via NavierStokes ͑NS͒ equations, with experimental results from the literature. Monoatomic argon and helium are considered. In this modeling a finite-difference scheme with second-order spatial accuracy is employed. For argon the calculated density thickness is in good agreement with the experimental results. For helium the NS results agree well with those from the bimodal model and with the few available experimental data. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1921267͔The strong gradients within a shock-wave lead to a number of associated effects of scientific and technological relevance which have attracted the attention of theoreticians and experimentalists for a long time. Though the main features of shock waves are well understood, much remains to be done to complete the prediction of their quantitative aspects. The structure of a stationary shock wave has often been employed as a testing problem for numerical models of rarefied gas flows. In this context the one-dimensional ͑1D͒ shock waves produced in atomic argon and helium have been usual test systems to check the numerical aspects of NavierStokes ͑NS͒ equations by comparison with experiment.From the work done around 1950-1965 it was claimed that the NS approach could yield a reliable description of the density profile of the shock waves just up to Mach number Maϳ 2. This is more or less in accordance with the general validity criteria for the continuum description, as obtained from the classical Chapman-Enskog expansion of Boltzmann equation. A discussion of these aspects has been given by Kogan, 1 Cercignani, 2 and others. [3][4][5] Moreover, due to the sparse experimental temperature and velocity data on welldefined 1D shock waves produced in shock tubes, little was known about the actual merits of NS equations to model the profiles of these quantities across the shock wave. This limitation has prevailed up to now in spite of the wealth of density and temperature data on 2D shock waves produced in jets. 6,7 Unfortunately, 2D flows pose a number of difficulties for numerical modeling of normal shock waves ͑complicated flow pattern, low temperature upstream of the shock, with poorly known dependence of the viscosity on the temperature͒. Therefore, 2D shock waves are not well suited for use in connection with the simple 1D mathematical formulation.The main source of experimental 1D shock-wave density data suited for the present purpose has been compiled and completed with accurate original data by Alsmeyer. 8 In this work the experimental reciprocal thickness of argon and helium 1D shock waves is shown to be well characterized up to Ma= 10, while a few sparse helium data points have been included. Complete argon experimental density profiles were also reported by Alsmeyer for several MaϽ 10 values. Due to the shortage of experimental data on helium, the results of bimodal calculations have been also used as a reference, 9 since they are known to be quite rel...

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“…[1][2][3][4][5] The reciprocal shock thickness in helium agrees reasonably well with the results of bimodal calculations 9 and with the few available experimental data.…”

Section: Salvador Monterosupporting

confidence: 75%

Section: Salvador Monteromentioning

confidence: 99%

Numerical simulation of shock-wave structure for argon and helium

2005

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“…The values of Ω(T ) (2,2) given in the appendix of Ref. [15] for this potential appear to be too large by a factor ≈ 1.27.…”

Section: Dsmc Models and Viscosity Formulaementioning

confidence: 99%

“…The shock thickness of argon, a monatomic gas for which there are no complications arising from energy exchange between rotational, vibrational and translational modes, has been measured by various experimentalists [2], [3], [4]. Typical results for shock thickness, at various Mach numbers, obtained from the Navier-Stokes equations are shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Viscosity of argon at temperatures >2000 K from measured shock thickness

Macrossan

Lilley

2003

Physics of Fluids

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Mott-Smith's approximate theory of plane 1D shock structure (Phys. Rev., 82, 885-92, 1951; Phys. Rev., 5, 1325-36, 1962 suggests, for any intermolecular potential, the average number of collisions undergone by a molecule as it cross the shock quickly approaches a limit as the Mach number increases. We check this with DSMC calculations and show that it can be used to estimate the gas viscosity at high temperatures from measurements of shock thickness. We consider a monatomic gas (γ = 5/3) for five different collision models and hence five different viscosity laws µ = µ (T ). The collision models are: the variable hard sphere, σ ∝ 1/g 2υ , with three values of υ; the generalized hard sphere; and the Maitland-Smith potential. For shock Mach numbers M 1 4.48, all these collision models predict a shock thickness ∆ = 11.0λ s , where λ s is a suitably defined 'shock length scale', with a scatter ≈ 2.5% (2 standard deviations). This shock length depends on the upstream flow speed, downstream density and a collision cross-section derived from the viscosity of the gas at a temperature T g , characteristic of the collisions at relative speed g = u 1 − u 2 between upstream and downstream molecules. Using ∆ = 11λ s and the experimental measurements of shock thickness in argon given by Alsmeyer (J. Fluid Mech. 74, 498-513, 1976), we estimate the viscosity of argon at high values of T g . These estimated values agree with the viscosity of argon recommended by the CRC Handbook of Chemistry and Physics (2001) at T ≈ 1, 500 K. For T 2, 000 K, for which there appears to be no reliable direct measurements of viscosity, our estimated values lie be- Taking the error in the experimental measurements of ∆ as the scatter in the results of Alsmeyer (± 2%), we estimate the uncertainty in the viscosity deduced from the shock thickness measurements as less than ± 5%. To this accuracy, our results agree with the power law predictions and disagree with the CRC Handbook values, for T 3,000 K.

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“…In the 1970s, rotational temperature was measured using the electron beam fluorescence method (EBFM) by some researchers (8), (9) , however, these measurements have mainly been conducted in a free-expansion jet or a normal shock wave. Therefore, there is little experimental data measured in the interaction between a shock wave and a boundary layer.…”

Section: Introductionmentioning

confidence: 99%

Interaction between Shock Wave and Boundary Layer in Nonequilibrium Hypersonic Rarefied Flow

Tsuboi

Matsumoto

2006

JSME international journal. Ser. B, Fluids and thermal engineer

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An experimental study of the interaction between a shock wave and a boundary layer over a flat plate with a sharp leading edge in hypersonic rarefied gas flow is presented. Experiments in a low-density wind tunnel using an electron beam probe were conducted at the Shock Wave Laboratory, RWTH Aachen, Germany. Rotational temperatures for stagnation temperatures of T 0 = 670∼1 000 K and Kn = 0.024∼0.028 based on a reference length of 0.05 m were calculated using Muntz's method and Robben and Talbot's method. The domain of quasi two-dimensional flow over the plate was determined from three-dimensional rotational temperature measurements. Nonequilibrium between translational and rotational temperatures was observed near the leading edge, and the experimental rotational relaxation length explains the rotational collision number of 2∼4.

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Measurement of Shock Wave Thickness by the Electron Beam Fluorescence Method

Cited by 116 publications

References 13 publications

Numerical simulation of shock-wave structure for argon and helium

Numerical simulation of shock-wave structure for argon and helium

Viscosity of argon at temperatures >2000 K from measured shock thickness

Interaction between Shock Wave and Boundary Layer in Nonequilibrium Hypersonic Rarefied Flow

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Measurement of Shock Wave Thickness by the Electron Beam Fluorescence Method

Cited by 116 publications

References 13 publications

Numerical simulation of shock-wave structure for argon and helium

Numerical simulation of shock-wave structure for argon and helium

Viscosity of argon at temperatures &gt;2000 K from measured shock thickness

Interaction between Shock Wave and Boundary Layer in Nonequilibrium Hypersonic Rarefied Flow

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Viscosity of argon at temperatures >2000 K from measured shock thickness