arXiv subjects

Matei I. Radulescu

Publications and source records attributed to Matei I. Radulescu.

At least 19 recordsLinked to original sources

arXiv2026

Quasi-Two-Dimensional Simulation of a Rotating Detonation Engine Combustor and Injector

A numerical simulation of an annular rotating detonation engine with stoichiometric hydrogen-oxygen is performed. A generic, well posed, and easily implemented approach using a quasi-two-dimensional method to model the area variations through the rotating detonation engine's injector and combustor is presented. The detonation--injector interaction is studied for the case with a ratio of four between the combustor and injector's throat areas. A shock wave is formed in the divergent portion of the injector due the high back pressure created by the detonation in the combustor. A Favre-averaged steady-state analysis of stream lines and particle paths reveals that the shock causes an irrecoverable loss of stagnation pressure. Stagnation pressure gain in the combustor is insufficient to make up for the loss and the flow leaves the engine with lower stagnation pressure than in the plenum.

physics.flu-dyn↗

arXiv2024

Role of the argon and helium bath gases on the structure of H2/O2 detonations

This study investigates the role of two inert mono-atomic diluents, argon and helium, on the detonation structure in order to assess the importance of vibrational non-equilibrium and wall losses. When relaxation effects and wall losses are neglected, the detonation waves in mixtures diluted with either of these gases have the same kinetics, Mach number, and specific heat ratio and hence are expected to lead to the same cellular dynamics. The experiments were conducted in 2H2/O2/7Ar and 2H2/O2/7He mixtures in a narrow channel. The initial pressure was adjusted in such a way that the induction zone length (therefore cell sizes) calculated from the ideal ZND model remained constant. The experiments revealed differences in velocity deficits and cell sizes despite maintaining a constant induction zone length across the mixtures. Near the detonation limits, the disparity in cell sizes between the two mixtures nearly doubled. We incorporated the boundary layer flow divergence in a perturbation analysis based on the square wave detonation assumption and established the controlling loss parameter as the product of the induction to channel size and the inverse of the square root of the Reynolds number. The very good collapse of the scaled results with the two bath gases with the loss parameter, and further comparison with 2D numerical simulations with account for flow divergence to the third dimension, confirmed the viscous loss mechanism to be dominating. Calculations suggest that the slower relaxation of H2 becomes comparable with the ignition delay anticipated from the ZND model and is slower by 70% in the argon diluted system. Differences possibly highlighting the role of non-equilibrium were not observed. This suggests the vibrational non-equilibrium effect may be less apparent in cellular detonations due to the lengthening of the ignition delays owing to the non-steady detonation structure.

physics.flu-dyn↗

arXiv2020

Dynamics of Hydrogen-oxygen-argon cellular detonations with a constant mean lateral strain rate

The present work revisits the problem of modelling the real gaseous detonation dynamics at the macro-scale by simple steady one-dimensional (1D) models. Experiments of detonations propagating in channels with exponentially expanding cross-sections were conducted in the H2/O2/Ar reactive system. Steady detonation waves were obtained at the macro-scale, with cellular structures characterized by reactive transverse waves. For all the mixtures studied, the dependence of the mean detonation speed was found to be in excellent agreement with first principles predictions of quasi-1D detonation dynamics with lateral strain rate predicted from detailed chemical kinetic models. This excellent agreement departs from the earlier experiments of Radulescu and Borzou (2018) in more unstable detonations. The excellent agreement is likely due to the much longer reaction zone lengths of argon diluted hydrogen-oxygen detonations at low pressures, as compared with the characteristic induction zone lengths. While the cellular instability modifies the detonation induction zone, the detonation dynamics at the macro-scale are arguably controlled by its hydrodynamic thickness. Near the limit, minor discrepancy is observed, with the experimental detonations typically continuing to propagate to slightly higher lateral strain rates and higher velocity deficits.

physics.flu-dyn↗

arXiv2020

Role of instability on the limits of laterally strained detonation waves

The present work examines the role of instability and diffusive phenomena in controlling the limits of detonations subject to lateral strain rates. Experiments were conducted in hydrocarbon-oxygen mixtures with varying levels of cellular instability. These detonations were propagated in channels with exponentially enlarging cross-sections, following the recent works of Radulescu \& Borzou (2018) and Xiao \& Radulescu (2020). Steady detonation waves were obtained at the macro-scale, with the near-limit reaction zone structures characterized by significant unreacted gas pockets. The turbulent flame burning velocity of these pockets was evaluated to be 30 m/s to 70 m/s, which is larger than the theoretical laminar value by a factor of 2 to 7. For all the mixtures tested, the characteristic $D-K$ relationships, relating the detonation mean propagation speed with lateral flow divergence, were obtained directly from experiments and as well from the generalized ZND model with lateral strain rates using detailed chemical kinetics. The results showed that the degree of departure between experiments and the theoretical predictions increases significantly with the detonation instability level. As compared to the laminar ZND wave, the more unstable detonations are much more detonable than the more stable detonations, with substantially larger limiting divergence rates and maximum velocity deficits. Such enhanced detonability with detonation instability can be manifested in the significantly enhanced global rates of energy release with the notably suppressed thermal character of ignition for the more unstable detonations. This globally enhanced burning mechanism is found to be realized by the intensified auto-ignition assisted by the turbulent diffusive burning of the unreacted gas pockets, substantially shortening the characteristic reaction zone lengths.

physics.flu-dyn↗

arXiv2020

Effect of boundary layer losses on 2D detonation cellular structures

We evaluate the effect of boundary layer losses on two-dimensional H2/O2/Ar cellular detonations obtained in narrow channels. The experiments provide the details of the cellular structure and the detonation speed deficits from the ideal CJ speed. We model the effect of the boundary layer losses by incorporating the flow divergence in the third dimension due to the negative boundary layer displacement thickness, modeled using Mirels' theory. The cellular structures obtained numerically with the resulting quasi-2D formulation of the reactive Euler equations with two-step chain-branching chemistry are found in excellent agreement with experiment, both in terms of cell dynamics and velocity deficits, provided the boundary layer constant of Mirels is modified by a factor of 2. A significant increase in the cell size is found with increasing velocity deficit. This is found to be very well captured by the induction zone increase in slower detonations due to the lower temperatures in the induction zone.

physics.flu-dyn↗

arXiv2020

Non-uniqueness of solutions in asymptotically self-similar shock reflections

The present study addresses the self-similar problem of unsteady shock reflection on an inclined wedge. The start-up conditions are studied by modifying the wedge corner and allowing for a finite radius of curvature. It is found that the type of shock reflection observed far from the corner, namely regular or Mach reflection, depends intimately on the start-up condition, as the flow "remembers" how it was started. Substantial differences were found. For example, the type of shock reflection for an incident shock Mach number $M=6.6$ and an isentropic exponent $γ=1.2$ changes from regular to Mach reflection between $44^\circ$ and $45^\circ$ when a straight wedge tip is used, while the transition for an initially curved wedge occurs between $57^\circ$ and $58^\circ$.

physics.flu-dyn↗

arXiv2019

Enhanced DDT mechanism from shock-flame interactions in thin channels

We show experimentally and numerically that when a weak shock interacts with a finger flame in a narrow channel, an extremely efficient mechanism for deflagration to detonation transition occurs. This is demonstrated in a 19-mm-thick channel in hydrogen-air mixtures at pressures below 0.2 atm and weak shocks of Mach numbers 1.5 to 2. The mechanism relies primarily on the straining of the flame shape into an elongated alligator flame maintained by the anchoring mechanism of Gamezo in a bifurcated lambda shock due to boundary layers. The mechanism can increase the flame surface area by more than two orders of magnitude without any turbulence on the flame time scale. The resulting alligator-shaped flame is shown to saturate near the Chapman-Jouguet condition and further slowly accelerate until its burning velocity reaches the sound speed in the shocked unburned gas. At this state, the lead shock and further adiabatic compression of the gas in the induction zone gives rise to auto-ignition and very rapid transition to detonation through merging of numerous spontaneous flames from ignition spots. The entire acceleration can occur on a time scale comparable to the laminar flame time.

physics.flu-dyn↗

arXiv2018

Mechanism of flame acceleration and detonation transition from the interaction of a supersonic turbulent flame with an obstruction

The present paper seeks to determine the mechanism of flame acceleration and transition to detonation when a turbulent flame preceded by a shock interacts with a single obstruction in its path, taken as a cylindrical obstacle or a wall in the present study. The problem is addressed experimentally in a mixture of propane-oxygen at sub-atmospheric conditions. The turbulent flame was generated by passing a detonation wave through a perforated plate, yielding flames with turbulent burning velocities 10 to 20 larger than the laminar values and incident shock Mach numbers ranging between 2 and 2.5. Time resolved schlieren videos recorded at approximately 100 kHz and numerical reconstruction of the flow field permitted to determine the mechanism of flame acceleration and transition to detonation. It was found to be the enhancement of the turbulent burning rate of the flame through its interaction with the shock reflection on the obstacle. The amplification of the burning rate was found to drive the flame burning velocity close to the speed of sound with respect to the fresh gases, resulting in the amplification of a shock in front of the flame. The acceleration through this regime resulted in the strengthening of this shock. Detonation was observed in regions of non-planarity of this internal shock, inherited by the irregular shape of the turbulent flame itself. Auto-ignition at early times of this process was found to be negligibly slow compared with the flow evolution time scale in the problem investigated, suggesting that the relevant time scale is primarily associated with the increase in turbulent burning rate by the interaction with reflected shocks.

physics.flu-dyn↗

arXiv2016

Thermal ignition revisited with two-dimensional molecular dynamics: role of fluctuations in activated collisions

The problem of thermal ignition in a homogeneous gas is revisited from a molecular dynamics perspective. A two-dimensional model is adopted, which assumes reactive disks of type A and B in a fixed area that react to form type C products if an activation threshold for impact is surpassed. Such a reaction liberates kinetic energy to the product particles, representative of the heat release. The results for the ignition delay are compared with those obtained from the continuum description assuming local thermodynamic equilibrium, in order to assess the role played by molecular fluctuations. Results show two regimes of non-equilibrium ignition whereby ignition occurs at different times as compared to that from the continuum description. The first regime is at low activation energies, where the ignition time is found to be higher than that expected from theory for all values of heat release, in agreement with predictions from Prigogine and Xhrouet who attribute this departure to non-equilibrium effects. Results suggest the ignition is spatially homogeneous in this regime. The second regime occurs at high activation energies and sufficiently large heat release values. In this regime, ignition times are found to be dependent on domain size, with larger domains yielding shorter ignition delays than expected. Results for larger systems agree with the expectations by Prigogine and Mahieu, who predict a non-equilibrium reaction rate larger than expected for a homogeneous system in equilibrium. Results yield a large variance for ignition times under these conditions, suggesting a departure from homogeneous combustion. The results obtained are in qualitative agreement with experimental observations of auto-ignition at relatively low temperatures, where hot-spot ignition and associated ignition delays lower than predicted are generally observed.

physics.chem-ph↗

arXiv2016

Influence of Turbulent Fluctuations on Detonation Propagation

The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane-oxygen cellular detonations in a thin channel geometry. The sufficiently high temporal resolution permitted to determine the PDF of the shock distribution, a power-law with an exponent of -3, and the burning rate of unreacted pockets from their edges - through surface turbulent flames with a speed approximately 3-7 times larger than the laminar one at the local conditions. Numerical simulations were performed using a novel Large Eddy Simulation method where the reactions due to both auto-ignition and turbulent transport and treated exactly at the sub-grid scale in a reaction-diffusion formulation. The model is an extension of Kerstein & Menon's Linear Eddy Model for Large Eddy Simulation to treat flows with shock waves and rapid gasdynamic transients. The two-dimensional simulations recovered well the amplification of the laminar flame speed owing to the turbulence generated mainly by the shear layers originating from the triple points and subsequent Richtmyer-Meshkov instability associated with the internal pressure waves. The simulations clarified how the level of turbulence generated controlled the burning rate of the pockets, the hydrodynamic thickness of the wave, the cellular structure and its distribution. Three-dimensional simulations were found in general good agreement with the two-dimensional ones, in that the sub-grid scale model captured the ensuing turbulent burning once the scales associated with the cellular dynamics, where turbulent kinetic energy is injected, are well resolved.

physics.flu-dyn↗

arXiv2016

Viscous solution of the triple shock reflection problem

The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier-Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition, when the gas was assumed to be inert. Viscosity was found to play an important role on some shock reflection mechanisms believed to accelerate reaction rates in detonations when time scales are small. A small wall jet was present in the double Mach reflection and increased in size with Reynolds number, eventually forming a small vortex. Kelvin-Helmholtz instabilities were absent and there was no Mach stem bifurcation at Reynolds numbers corresponding to when the Mach stem had travelled distances on the scale of the induction length. Kelvin-Helmholtz instabilities are found to not likely be a source of rapid reactions in detonations at time scales commensurate with the ignition delay behind the Mach stem.

physics.flu-dyn↗

arXiv2015

Chapman-Jouguet deflagrations and their transition to detonation

We study experimentally fast flames and their transition to detonation in mixtures of methane, ethane, ethylene, acetylene, and propane mixtures with oxygen. Following the interaction of a detonation wave with a column of cylinders of varying blockage ratio, the experiments demonstrate that the fast flames established are Chapman-Jouguet deflagrations, in excellent agreement with the self-similar model of Radulescu et al. (2015). The experiments indicate that these Chapman-Jouguet deflagrations dynamically restructure and amplify into fewer stronger modes until the eventual transition to detonation. The transition length to a self-sustained detonation was found to correlate very well with the mixtures' sensitivity to temperature fluctuations, reflected by the $χ$ parameter introduced by Radulescu, which is the product of the non-dimensional activation energy $E_a/RT$ and the ratio of chemical induction to reaction time $t_i/t_r$. Correlation of the measured DDT lengths determined that the relevant characteristic time scale from chemical kinetics controlling DDT is the energy release or excitation time $t_r$. Correlations with the cell size also capture the dependence of the DDT length on $χ$ for fixed blockage ratios.

physics.flu-dyn↗

arXiv2015

Evolution and stability of shock waves in dissipative gases characterized by activated inelastic collisions

Previous experiments have revealed that shock waves driven through dissipative gases may become unstable, for example, in granular gases, and in molecular gases undergoing strong relaxation effects. The mechanisms controlling these instabilities are not well understood. We successfully isolated and investigated this instability in the canonical problem of piston driven shock waves propagating into a medium characterized by inelastic collision processes. We treat the standard model of granular gases, where particle collisions are taken as inelastic with constant coefficient of restitution. The inelasticity is activated for sufficiently strong collisions. Molecular dynamic simulations were performed for 30,000 particles. We find that all shock waves investigated become unstable, with density non-uniformities forming in the relaxation region. The wavelength of these fingers is found comparable to the characteristic relaxation thickness. Shock Hugoniot curves for both elastic and inelastic collisions were obtained analytically and numerically. Analysis of these curves indicate that the instability is not of the Bethe-Zeldovich-Thompson or Dyakov-Kontorovich types. Analysis of the shock relaxation rates and rates for clustering in a convected fluid element with the same thermodynamic history outruled the clustering instability of a homogeneous granular gas. Instead, wave reconstruction of the early transient evolution indicates that the onset of instability occurs during the re-pressurization of the gas following the initial relaxation of the medium behind the lead shock. This re-pressurization gives rise to internal pressure waves in the presence of strong density gradients. This indicates that the mechanism of instability is more likely of the vorticity-generating Richtmyer-Meshkov type, relying on the action of the inner pressure waves development during the transient relaxation.

cond-mat.soft↗

arXiv2014

A nonlinear evolution equation for pulsating detonations using Fickett's model with chain branching kinetics

The detonation wave stability is addressed using Fickett's equation, i.e., the reactive form of Burgers' equation. This serves as a simple analogue to the reactive Euler equations, permitting one to gain insight into the nonlinear dynamics of detonation waves. Chemical kinetics were modeled using a two-step reaction with distinct induction and reaction zones. An evolution equation for the detonation structure was derived using the method of matched asymptotics for large activation energy and slow rate of energy release. While the first order solution was found unconditionally unstable, the second order evolution equation predicted both stable and unstable solutions. The neutral stability boundary was found analytically, given by $χ=4$, where $χ$ is the product of activation energy and the ratio of induction to reaction time. This reproduces accurately what has been previously established for the reactive Euler equations and verified experimentally. The evolution equation also captures stable limit cycle oscillations in the unstable regime and offers unique insight into the instability mechanism. The mechanism amplifying the perturbations lies within the induction zone, where the Arrhenius-type rate equation provides a large change in induction times for small perturbations. The mechanism attenuating the perturbations arises from acoustic effects, which delays the amplification of the shock front. The longer the detonation wave, the more time it takes for the amplification from the reaction zone to reach the shock front, creating gradients that counter-act the amplification from the flame acceleration. The results agree with direct numerical simulation, as well as recovering many similarities with the reactive Euler equation.

physics.flu-dyn↗

arXiv2012

Dynamics of unconfined spherical flames

Using the soap bubble technique, we visualize the dynamics of unconfined hydrogen-air flames using high speed schlieren video. We show that for sufficiently weak mixtures, i.e., low flame speeds, buoyancy effects become important. Flame balls of a critical dimension begin to rise. The experiments are found in very good agreement with the scaling laws proposed by Zingale and Dursi. We report the results in a fluid dynamics video.

physics.flu-dyn↗

arXiv2012

Shock instability in dissipative gases

Previous experiments have revealed that shock waves in thermally relaxing gases, such as ionizing, dissociating and vibrationally excited gases, can become unstable. To date, the mechanism controlling this instability has not been resolved. Previous accounts of the D'yakov-Kontorovich instability, and Bethe-Zel'dovich-Thompson behaviour could not predict the experimentally observed instability. To address the mechanism controlling the instability, we study the propagation of shock waves in a simple two-dimensional dissipative hard disk molecular model. To account for the energy relaxation from translational degrees of freedom to higher modes within the shock wave structure, we allow inelastic collisions above an activation threshold. When the medium allows finite dissipation, we find that the shock waves are unstable and form distinctive high density non-uniformities and convective rolls on their surface. Using analytical and numerical results for the shock Hugoniot, we show that both DK and BZT instabilities can be ruled out. Instead, the results suggest that the clustering instability of Goldhirsch and Zanetti in dissipative gases is the dominant mechanism.

nlin.PS↗

arXiv2012

Dynamics of shock induced ignition in Fickett's model with chain-branching kinetics: influence of $χ$

The problem of shock induced ignition by a piston is addressed in the framework of Fickett's model for reactive compressible flows, i.e., the reactive form of Burgers' equation. An induction-reaction two-step chain-branching model is used to study the coupling between the energy release and the compressible hydrodynamics occurring during the shock ignition transient leading to a detonation. Owing to the model's simplicity, the ignition and acceleration mechanism is explained using the two families of characteristics admitted by the model. The energy release along the particle paths provides the amplification of forward-travelling pressure waves. These waves pre-compress the medium in the induction layer ahead of the reaction zone, therefore changing the induction delays of successive particles. The variation of the induction delay provides the modulation of the amplification of the forward travelling pressure waves by controlling the residence time of the pressure waves in the reaction zone. A closed form analytical solution is obtained by the method of characteristics and high activation energy asymptotics. The acceleration of the reaction zone was found to be proportional to the product of the activation energy, the ratio of the induction to reaction time and the heat release. This finding provides a theoretical justification for the previous use of this non-dimensional number to characterize the ignition regimes observed experimentally in detonations and shock induced ignition phenomena. Numerical simulations are presented and analysed. Both subsonic and supersonic internal flame propagation regimes are observed, consistent with experiment and previous reactive Euler models.

math-ph↗

arXiv2011

Shock Waves in Dense Hard Disk Fluids

Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock dynamics are studied for a two-dimensional hard-disk medium at both the continuum and discrete particle level descriptions. For the continuum description, closed form analytical expressions for the inviscid hydrodynamic description, shock Hugoniot, isentropic exponent and shock jump conditions were obtained using the Helfand equation of state. The closed-form analytical solutions permitted us to gain physical insight on the role of the material's density on its compressibility, i.e. how the medium compresses under mechanical loadings and sustains wave motion. Furthermore, the predictions were found in excellent agreement with calculations using the Event Driven Molecular Dynamic method involving 30,000 particles over the entire range of compressibility spanning the dilute ideal gas and liquid phases. In all cases, it was found that the energy imparted by the piston motion to the thermalized medium behind the propagating shock was quasi-independent of the medium's packing fraction, with a correction vanishing with increasing shock Mach numbers.

physics.flu-dyn↗