Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam

Alsmeyer, H.

doi:10.1017/s0022112076001912

Cited by 407 publications

(377 citation statements)

References 21 publications

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“…A well-known feature of CFD solvers is the artificial steepening of viscous shock profiles; it is also well-established that DSMC predicts shock profiles accurately [31,42]. At times t 2 through t 6 , we see a steepness discrepancy between the ensemble hybrid profile and the ensemble PDE-only profile.…”

Section: Non-equilibrium System: Strong Moving Shockmentioning

confidence: 88%

Algorithm Refinement for Fluctuating Hydrodynamics

Williams¹,

Bell²,

Garcia³

2008

Multiscale Model. Simul.

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This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle al-1 gorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau-Lifshitz Navier-Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently-developed solver for LLNS, based on third-order Runge-Kutta. We present numerical tests of systems in and out of equilibrium, including timedependent systems, and demonstrate dynamic adaptive refinement by the computation of a moving shock wave. Mean system behavior and second moment statistics of our simulations match theoretical values and benchmarks well. We find that particular attention should be paid to the spectrum of the flux at the interface between the particle and continuum methods, specifically for the non-hydrodynamic (kinetic) time scales.

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Section: Non-equilibrium System: Strong Moving Shockmentioning

confidence: 88%

Algorithm Refinement for Fluctuating Hydrodynamics

Williams¹,

Bell²,

Garcia³

2008

Multiscale Model. Simul.

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“…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.…”

Section: Salvador Monteromentioning

confidence: 99%

“…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 reliable for shock-wave modeling. 10 In the present work the calculations of 1D shock-wave structures have been carried out by employing the NS equations, the results being compared with the referred experimental data 8 and bimodal model. 9,10 Neither the velocity nor the temperature profiles were measured in the former experiments.…”

Section: Salvador Monteromentioning

confidence: 99%

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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“…The dynamics of normal shock waves, similar to the Mach disk of supersonic jets, has been widely studied in one dimension, theoretically (Mott-Smith 1951), numerically (Koura 1997) using the direct simulation Monte Carlo method (DSMC) developed by Bird (1994), and experimentally (Robben & Talbot 1966a, b;Alsmeyer 1976;Pham-Van-Diep, Erwin & Muntz 1989).…”

Section: Introductionmentioning

confidence: 99%

Experimental and numerical investigation of an axisymmetric supersonic jet

et al. 2001

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A comprehensive study of a steady axisymmetric supersonic jet of CO 2 , including experiment, theory, and numerical calculation, is presented. The experimental part, based on high-sensitivity Raman spectroscopy mapping, provides absolute density and rotational temperature maps covering the significant regions of the jet: the zone of silence, barrel shock, Mach disk, and subsonic region beyond the Mach disk. The interpretation is based on the quasi-gasdynamic (QGD) system of equations, and its generalization (QGDR) considering the translational-rotational breakdown of thermal equilibrium. QGD and QGDR systems of equations are solved numerically in terms of a finite-difference algorithm with the steady state attained as the limit of a time-evolving process. Numerical results show a good global agreement with experiment, and provide information on those quantities not measured in the experiment, like velocity field, Mach numbers, and pressures. According to the calculation the subsonic part of the jet, downstream of the Mach disk, encloses a low-velocity recirculation vortex ring.

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Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam

Cited by 407 publications

References 21 publications

Algorithm Refinement for Fluctuating Hydrodynamics

Algorithm Refinement for Fluctuating Hydrodynamics

Numerical simulation of shock-wave structure for argon and helium

Experimental and numerical investigation of an axisymmetric supersonic jet

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