5 results
Structure and stability of shock waves in granular gases
- Nick Sirmas, Matei I. Radulescu
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- Journal:
- Journal of Fluid Mechanics / Volume 873 / 25 August 2019
- Published online by Cambridge University Press:
- 25 June 2019, pp. 568-607
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Previous experiments have revealed that shock waves driven through dissipative media may become unstable, for example, in granular gases, and in molecular gases undergoing strong relaxation effects. The current paper addresses this problem of shock stability at the Euler and Navier–Stokes continuum levels in a system of disks (two-dimensional) undergoing activated inelastic collisions. The dynamics of shock formation and stability is found to be in very good agreement with earlier molecular dynamic simulations (Sirmas & Radulescu, Phys. Rev. E, vol. 91, 2015, 023003). It was found that the modelling of shock instability requires the introduction of molecular noise for its development and sustenance. This is confirmed in two stability problems. In the first, the evolution of shock formation dynamics is monitored without noise, with only initial noise and with continuous molecular noise. Only the latter reproduces the results of shock instability of molecular dynamics simulations. In the second problem, the steady travelling wave solution is obtained for the shock structure in the inviscid and viscous limits and its nonlinear stability is studied with and without molecular fluctuations, again showing that instability can be sustained only in the presence of fluctuations. The continuum results show that instability takes the form of a rippled front of a wavelength comparable with the relaxation thickness of the steady shock wave, at scales at which molecular fluctuations become important, in excellent agreement with the molecular dynamic simulations.
Dynamics of detonations with a constant mean flow divergence
- Matei I. Radulescu, Bijan Borzou
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- Journal:
- Journal of Fluid Mechanics / Volume 845 / 25 June 2018
- Published online by Cambridge University Press:
- 25 April 2018, pp. 346-377
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An exponential horn geometry is introduced in order to establish cellular detonations with a constant mean lateral mass divergence, propagating at quasi-steady speeds below the Chapman–Jouguet value. The experiments were conducted in $2\text{C}_{2}\text{H}_{2}+5\text{O}_{2}+21\text{Ar}$ and $\text{C}_{3}\text{H}_{8}+5\text{O}_{2}$. Numerical simulations were also performed for weakly unstable cellular detonations to test the validity of the exponential horn geometry. The experiments and simulations demonstrated that such quasi-steady state detonations can be realized, hence permitting us to obtain the relations between the detonation speed and mean lateral flow divergence for cellular detonations in an unambiguous manner. The experimentally obtained speed ($D$) dependencies on divergence ($K$) were compared with the predictions for steady detonations with lateral flow divergence obtained with the real thermo-chemical data of the mixtures. For the $2\text{C}_{2}\text{H}_{2}+5\text{O}_{2}+21\text{Ar}$ system, reasonable agreement was found between the experiments and steady wave prediction, particularly for the critical divergence leading to failure. Observations of the reaction zone structure in these detonations indicated that all the gas reacted very close to the front, as the transverse waves were reactive. The experiments obtained in the much more unstable detonations in $\text{C}_{3}\text{H}_{8}+5\text{O}_{2}$ showed significant differences between the experimentally derived $D(K)$ curve and the prediction of steady wave propagation. The latter was found to significantly under-predict the detonability of cellular detonations. The transverse waves in this mixture were found to be non-reactive, hence permitting the shedding of non-reacted pockets, which burn via turbulent flames on their surface. It is believed that the large differences between experiment and the inviscid model in this class of cellular structures is due to the importance of diffusive processes in the burn-out of the non-reacted pockets. The empirical tuning of a global one-step chemical model to describe the macro-scale kinetics in cellular detonations revealed that the effective activation energy was lower by 14 % in $2\text{C}_{2}\text{H}_{2}+5\text{O}_{2}+21\text{Ar}$ and 54 % in the more unstable $\text{C}_{3}\text{H}_{8}+5\text{O}_{2}$ system. This confirms previous observations that diffusive processes in highly unstable detonations are responsible for reducing the thermal ignition character of the gases processed by the detonation front.
The mechanism of detonation attenuation by a porous medium and its subsequent re-initiation
- MATEI I. RADULESCU, BRIAN McN. MAXWELL
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- Journal:
- Journal of Fluid Mechanics / Volume 667 / 25 January 2011
- Published online by Cambridge University Press:
- 14 January 2011, pp. 96-134
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The attenuation and re-initiation mechanism of detonations transmitted through a porous section consisting of a two-dimensional array of staggered cylinders was investigated experimentally and numerically for acetylene–oxygen mixtures. It was found that the leading order attenuation mechanism is the wave diffraction around the cylinders. The local re-amplification permitting the self-propagation of the wave was due to wave reflections from adjacent obstacles. The critical conditions for transmittance of a detonation wave were found to correspond approximately to a pore size equal to approximately 30–60 detonation induction lengths, or one to two cell sizes. For quenched detonations, the re-initiation mechanism was found to rely on wave reflections from neighbouring pores. Depending on the mixture sensitivity, one or several shock reflections may be necessary to re-amplify the attenuated detonation wave back to a self-sustained wave. For the latter case, a novel mechanism was identified, where each shock reflection gives rise to a significant enhancement of the gas reactivity and burnout of large portions of unreacted gas. This leads to a slow acceleration of the leading front, punctuated by small-scale local sudden re-accelerations. The resulting wave interactions give rise to a topologically complex reaction zone structure consisting of alternating layers of reacted and unreacted gas. The role of turbulent diffusive burning during this transient is discussed.
The hydrodynamic structure of unstable cellular detonations
- MATEI I. RADULESCU, GARY J. SHARPE, CHUNG K. LAW, JOHN H. S. LEE
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- Journal of Fluid Mechanics / Volume 580 / 10 June 2007
- Published online by Cambridge University Press:
- 21 May 2007, pp. 31-81
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The study analyses the cellular reaction zone structure of unstable methane–oxygen detonations, which are characterized by large hydrodynamic fluctuations and unreacted pockets with a fine structure. Complementary series of experiments and numerical simulations are presented, which illustrate the important role of hydrodynamic instabilities and diffusive phenomena in dictating the global reaction rate in detonations. The quantitative comparison between experiment and numerics also permits identification of the current limitations of numerical simulations in capturing these effects. Simulations are also performed for parameters corresponding to weakly unstable cellular detonations, which are used for comparison and validation. The numerical and experimental results are used to guide the formulation of a stochastic steady one-dimensional representation for such detonation waves. The numerically obtained flow fields were Favre-averaged in time and space. The resulting one-dimensional profiles for the mean values and fluctuations reveal the two important length scales, the first being associated with the chemical exothermicity and the second (the ‘hydrodynamic thickness’) with the slower dissipation of the hydrodynamic fluctuations, which govern the location of the average sonic surface. This second length scale is found to be much longer than that predicted by one-dimensional reaction zone calculations.
The transient start of supersonic jets
- MATEI I. RADULESCU, CHUNG K. LAW
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- Journal:
- Journal of Fluid Mechanics / Volume 578 / 10 May 2007
- Published online by Cambridge University Press:
- 26 April 2007, pp. 331-369
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This study investigates the initial transient hydrodynamic evolution of highly under-expanded slit and round jets. A closed-form analytic similarity solution is derived for the temporal evolution of temperature, pressure and density at the jet head for vanishing diffusive fluxes, generalizing a previous model of Chekmarev using Chernyi's boundary-layer method for hypersonic flows. Two-dimensional numerical simulations were also performed to investigate the flow field during the initial stages over distances of ~ 1000 orifice radii. The parameters used in the simulations correspond to the release of pressurized hydrogen gas into ambient air, with pressure ratios varying between approximately 100 and 1000. The simulations confirm the similarity laws derived theoretically and indicate that the head of the jet is laminar at early stages, while complex acoustic instabilities are established at the sides of the jet, involving shock interactions within the vortex rings, in good agreement with previous experimental findings. Very good agreement is found between the present model, the numerical simulations and previous experimental results obtained for both slit and round jets during the transient establishment of the jet. Criteria for Rayleigh–Taylor instability of the decelerating density gradients at the jet head are also derived, as well as the formulation of a model addressing the ignition of unsteady expanding diffusive layers formed during the sudden release of reactive gases.