Nonclassical Dynamics of Classical Gases

Cramer, M. S.

doi:10.1007/978-3-7091-2608-0_5

Cited by 76 publications

(57 citation statements)

References 41 publications

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“…Van der Waals and Mie-Grüneisen models are simple models to investigate phenomena related to negative nonlinearity 1,[15][16][17]29,34,35 . We particularize the study for each non-convex model performing numerical experiments showing the anomalous wave phenomena that appears in the evolution of specific Riemann problems proposed in the literature for hydrodynamic codes.…”

Section: Numerical Examples Of Anomalous Wave Structure In Magnetmentioning

confidence: 99%

“…The analysis of the wave structure in the evolution of classical hydrodynamics described by Euler equations closed with a non-ideal EOS has been widely studied in the literature 1,13,14,[28][29][30][31][32] . It is well known that the structure and dynamics of waves are deter-mined by the properties of the material through a thermodynamic magnitude, the funda-…”

mentioning

confidence: 99%

“…Then isentropes lose convexity implying a loss of genuine nonlinearity of the acoustic waves and a negative value of the fundamental derivative. The acoustic wave family becomes more complex and the solution may generate anomalous structures like shock waves attached to an expansion fan, double shocks separated by a rarefaction fan and double rarefaction fans separated by a shock wave 29,32,34,35 . The emerging of composite wave structures (typical in non-convex dynamics) where shocks break expansion fans might not be a desirable effect in some applications.…”

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confidence: 99%

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Anomalous wave structure in magnetized materials described by non-convex equations of state

Serna

Marquina

2014

Physics of Fluids

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We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynamic properties of the material and the magnetic field as well as its possible rotation. We demonstrate that phase transitions induced by material properties do not necessarily imply the loss of genuine nonlinearity of the wavefields as is the case in classical hydrodynamics. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. In the examples we show how to determine the appropriate amount of magnetic field in the initial conditions of the Riemann problem to transform a thermodynamic composite wave into a simple nonlinear wave.

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Section: Numerical Examples Of Anomalous Wave Structure In Magnetmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Anomalous wave structure in magnetized materials described by non-convex equations of state

Serna

Marquina

2014

Physics of Fluids

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“…Thanks to its simplicity, the van der Waals model with constant c v (also referred to as the polytropic van der Waals model) has frequently been employed in studies on negative and mixed nonlinearities (see, e.g. Cramer & Sen 1986;Cramer 1991;Argrow 1996;Brown & Argrow 1997;Müller & Voß 2006). Indeed, as pointed out by many authors (see, e.g.…”

Section: Problem Formulationmentioning

confidence: 99%

“…If the shock is sufficiently close to the throat, as in 294 A. Guardone and D. Vimercati case R NC 2a (5), the resultant subsonic compression eventually attains a sonic point and a further shock, with sonic upstream state, must be formed to continue the flow. Following Kluwick (1993) and Cramer & Fry (1993), we will refer to this double compression-shock configuration as a split shock, owing to the analogies with the shock-splitting phenomenon in unsteady flows (see Wendroff 1972;Menikoff & Plohr 1989;Cramer 1991). According to relation (3.3), if the leading compression shock moves downstream the corresponding entropy jump increases.…”

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Exact solutions to non-classical steady nozzle flows of Bethe–Zel’dovich–Thompson fluids

Guardone

Vimercati

2016

J. Fluid Mech.

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Steady nozzle flows of Bethe-Zel'dovich-Thompson fluids -substances exhibiting non-classical gasdynamic behaviour in a finite vapour-phase thermodynamic region in close proximity to the liquid-vapour saturation curve -are examined. Non-classical flow features include rarefaction shock waves, shock waves with either upstream or downstream sonic states and split shocks. Exact solutions for a mono-component single-phase fluid expanding from a reservoir into a stationary atmosphere through a conventional converging-diverging nozzle are determined within the quasi-onedimensional inviscid flow approximation. The novel analytical approach makes it possible to elucidate the connection between the adiabatic, possibly non-isentropic flow field and the underlying local isentropic-flow features, including the possible qualitative alterations in passing through shock waves. Contrary to previous predictions based on isentropic-flow inspection, shock disintegration is found to occur also from reservoir states corresponding to a single sonic point. The global layout of the flow configurations produced by a monotonic decrease in the ambient pressure, namely the functioning regime, is examined for reservoir conditions resulting in single-phase flows. Accordingly, a classification of steady nozzle flows into 10 different functioning regimes is proposed. Flow conditions determining the transition between the different classes of flow are investigated and each functioning regime is associated with the corresponding thermodynamic region of reservoir states.

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Numerical simulation of dense gas flows on unstructured grids with an implicit high resolution upwind Euler solver

Colonna

Rebay

2004

Numerical Methods in Fluids

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The study of the dense gas flows which occur in many technological applications demands for fluid dynamic simulation tools incorporating complex thermodynamic models that are not usually available in commercial software. Moreover, the software mentioned can be used to study very interesting phenomena that usually go under the name of ‘non-classical gasdynamics’, which are theoretically predicted for high molecular weight fluids in the superheated region, close to saturation. This paper presents the numerical methods and models implemented in a computer code named zFlow which is capable of simulating inviscid dense gas flows in complex geometries. A detailed description of the space discretization method used to approximate the Euler equations on unstructured grids and for general equations of state, and a summary of the thermodynamic functions required by the mentioned formulation are also given. The performance of the code is demonstrated by presenting two applications, the calculation of the transonic flow around an airfoil computed with both the ideal gas and a complex equation of state and the simulation of the non-classical phenomena occurring in a supersonic flow between two staggered sinusoidal blades. Non-classical effects are simulated in a supersonic flow of a siloxane using a Peng–Robinson-type equation of state. Siloxanes are a class of substances used as working fluids in organic Rankine cycles turbines

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Nonclassical Dynamics of Classical Gases

Cited by 76 publications

References 41 publications

Anomalous wave structure in magnetized materials described by non-convex equations of state

Anomalous wave structure in magnetized materials described by non-convex equations of state

Exact solutions to non-classical steady nozzle flows of Bethe–Zel’dovich–Thompson fluids

Numerical simulation of dense gas flows on unstructured grids with an implicit high resolution upwind Euler solver

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