Shock-wave-like structures induced by an exothermic neutralization reaction in miscible fluids (original) (raw)
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Structure of a Shock-Wave Front in a Liquid
Physical Review Letters, 1979
Solutions of the Navier-Stokes equations for strong shock waves in a dense fluid agree well with recent atomistic simulations using nonequilibrium molecular dynamics.
2010
The nonlinear evolution of two fluid interfacial structures like bubbles and spikes arising due to the combined action of Rayleigh-Taylor and Kelvin-Helmholtz instability or due to that of Richtmyer-Meshkov and Kelvin-Helmholtz instability resulting from oblique shock is investigated. Using Layzer's model analytic expressions for the asymptotic value of the combined growth rate are obtained in both cases for spikes and bubbles. However, if the overlying fluid is of lower density the interface perturbation behaves in different ways. Depending on the magnitude of the velocity shear associated with Kelvin-Helmholtz instability both the bubble and spike amplitude may simultaneously grow monotonically (instability) or oscillate with time or it may so happen that while this spike steepens the bubble tends to undulate. In case of an oblique shock which causes combined action of Richtmyer-Meshkov instability arising due to the normal component of the shock and Kelvin Helmholtz instability through creation of velocity shear at the two fluid interface due to its parallel component, the instability growth rate-instead of behaving as 1/t1/t1/t as trightarrowinftyt \rightarrow \inftytrightarrowinfty for normal shock, tends asymptotically to a spike peak height growth velocity simsqrtfrac5(1+AT)16(1−AT)(Deltav)2\sim \sqrt{\frac{5(1+A_{T})}{16(1-A_{T})}(\Delta v)^2}simsqrtfrac5(1+AT)16(1−AT)(Deltav)2 where Deltav\Delta v Deltav is the velocity shear and ATA_TAT is the Atwood number. Implication of such result in connection with generation of spiky fluid jets in astrophysical context is discussed.
Shock Wave Interactions with Exothermic Mixtures
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Shock formation in the presence of entropy gradients in fluids exhibiting mixed nonlinearity
Physics of Fluids, 2004
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Collision of localized traveling-wave convection cells in binary fluid
We study the collision processes of spatially localized traveling wave(pulses) in convection of binary fluid mixture by an amplitude equation. Qualitative result of pulse collision observed in experiments, the formation of bound states and pulse destruction, is reproduced by this equation. It is shown that even if the pulse collision results in the destruction of one pulse, bound state exists as a solution. We found that an unstable solution is embedded in the collision process, which is a candidate for "scattor", the unstable saddle near which orbits pass through and are sorted out along their unstable manifolds.
Shockwaves and Local Hydrodynamics: Failure of the Navier-Stokes Equations
Festschrift in Honor of Leopoldo García-Colín's 80th Birthday, 2010
Shockwaves provide a useful and rewarding route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear transport properties makes plain the connection between the observed local hydrodynamic variables (like the various gradients and fluxes) and the chosen recipes for defining (or "measuring") those variables. The range over which nonlocal hydrodynamic averages are computed turns out to be much more significant than are the other details of the averaging algorithms. The results show clearly the incompatibility of microscopic time-reversible cause-and-effect dynamics with macroscopic instantaneously-irreversible models like the Navier-Stokes equations.
Local equilibrium in liquid phase shock waves
Physical Review E
We have assessed the assumption of local thermodynamic equilibrium in a shock wave by comparing local thermodynamic data generated with nonequilibrium molecular dynamics (NEMD) simulations with results from corresponding equilibrium simulations. The shock had a Mach number approximately equal to 2 in a Lennard-Jones spline liquid. We found that the local equilibrium assumption holds perfectly well behind the wave front, and is a very good approximation in the front itself. This was supported by calculations of the excess entropy production in the shock front with four different methods that use the local equilibrium assumption in different ways. Two of the methods assume local equilibrium between excess thermodynamic variables by treating the shock as an interface in Gibbs's sense. The other two methods are based on the local equilibrium assumption in a continuous description of the shock front. We show for the shock studied in this work that all four methods give excess entropy productions that are in excellent agreement, with an average variance of 3.5% for the nonequilibrium molecular dynamics (NEMD) simulations. In addition, we solved the Navier-Stokes (N-S) equations numerically for the same shock wave using an equilibrium equation of state (EoS) based on a recently developed perturbation theory. The results for the density, pressure, and temperature profiles agree well with the profiles from the NEMD simulations. For instance, the shock waves generated in the two simulations travel with almost the same speed; the average absolute Mach-number deviation of the N-S simulations relative to NEMD is 2.6% in the investigated time interval.
On the Structure of Shock Waves in a Two-Phase Isothermal Model
2007
A traveling wave analysis of a two phase isothermal Euler model is performed in this work. This analysis allows to exhibit the inner structure of shock waves in two-phase flows. In the model under investigation, the dissipative regularizing term is not of viscous type but instead comes from relaxation phenomena toward equilibrium between the phases. This gives an unusual structure to the diusion tensor where dissipative terms appear only in the mass conservation equations. We show that this implies that the mass fractions are not constant inside the shock although the Rankine-Hugoniot relations give a zero jump of the mass fraction through the discontinuities. We also show that there exists a critical speed for the traveling waves above which no C 1 solutions exist. Neverthless for this case, it is possible to construct traveling solutions
Nondissipative shock waves in two-phase flows
Physica D: Nonlinear Phenomena, 1994
It is shown that the Korteweg-de Vries equation which describes dissipationless processes can occur also in the system of equations of multiphase hydrodynamics when dissipation is compensated by external supply of energy. Therefore all the phenomena which are characteristic for the Korteweg-de Vries equation (solitons, periodic waves, nondissipative shock waves) can occur also in multiphase hydrodynamics. The study analyzes in particular the phenomenon of formation of nondissipative shock waves. It is shown that multiphase filtration is accompanied by formation of a continuously expanding region with small scale undamping oscillations of phase composition and velocity. The analysis uses the Korteweg-de Vries equation which is derived from the system of conservation laws describing multiphase hydrodynamics in porous media. Obtained results are relevant for the analysis of multiphase filtration (viscous fingering in the hydrocarbon recovery process) and in the hydrodynamics of fluidized bed (formation of bubbles).