Turbulent Shock Research Articles

Experimental Investigation of Turbulent Flame Propagation and Pressure Oscillation in a Constant Volume Chamber Equipped With an Orifice Plate

ABSTRACTIn this work, the main contribution is an understanding of different combustion phenomena involving flame acceleration, flame propagation, and the pressure oscillation resulting from flame-shock interactions. These physical phenomena were experimentally studied using a newly developed confined combustion chamber equipped with one or two orifice plates. The results showed that there are five stages of flame propagation when a laminar flame passes through the orifice plate in a confined space. These include the deceleration of the laminar flame, jet flame formation and rapid acceleration, deceleration of the flame, turbulent flame formation and acceleration, and turbulent flame propagation in the end-gas region. Flame acceleration and pressure oscillation were found to be strongly related to the aperture size of the orifice plate. The high amplitudes of pressure oscillations were found to be the results of two combustion mechanisms: the end gas auto-ignition and the interactions between the accelerated turbulent flame and shock wave. To further accelerate the flame and promote stronger disturbance in the end gas, another identical orifice plate was employed. Subsequently, strong flame-shock interaction caused end-gas auto-ignition with an extremely high-amplitude pressure oscillation. Eventually, the maximum amplitude of pressure oscillation exceeded 8 MPa as end-gas auto-ignition occurred in the end region of the combustion chamber.

Numerical study of variable density turbulence interaction with a normal shock wave

Accurate numerical simulations of shock–turbulence interaction (STI) are conducted with a hybrid monotonicity-preserving–compact-finite-difference scheme for a detailed study of STI in variable density flows. Theoretical and numerical assessments of data confirm that all turbulence scales as well as the STI are well captured by the computational method. Linear interaction approximation (LIA) convergence tests conducted with the shock-capturing simulations exhibit a similar trend of converging to LIA predictions to shock-resolving direct numerical simulations (DNS). The effects of density variations on STI are studied by comparing the results corresponding to an upstream multi-fluid mixture with the single-fluid case. The results show that for the current parameter ranges, the turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist. Turbulent mixing enhancement by the shock is also increased and stronger mixing asymmetry in the postshock region is observed when there is significant density variation. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions having different densities. The dominant mechanisms behind the variable density STI are identified by analysing the transport equations for the Reynolds stresses, vorticity, normalized mass flux and density specific volume covariance.

Variable Turbulent Prandtl Number Model for Shock/Boundary-Layer Interaction

Interaction of shock waves with turbulent boundary layers can enhance the surface heat flux dramatically. Reynolds-averaged Navier–Stokes simulations based on a constant turbulent Prandtl number often give grossly erroneous heat transfer predictions in shock/boundary-layer interaction flows. This is due to the fact that the underlying Morkovin’s hypothesis breaks down in the presence of shock waves; thus, the turbulent Prandtl number cannot be assumed to be a constant. In this paper, a new variable turbulent Prandtl number model based on linearized Rankine–Hugoniot conditions applied to shock–turbulence interaction is developed. The turbulent Prandtl number is a function of the shock strength, and a shock function is proposed to identify the location and strength of shock waves. The shock function also simulates the postshock relaxation of the turbulent heat flux, which is akin to that observed in canonical shock–turbulence interaction. The model is combined with the well-validated shock-unsteadiness model and is applied to the complex shock topology observed in oblique shock/turbulent boundary-layer interactions. Comparison with experimental data shows significant improvement in the surface heat transfer rate in the interaction region, both for attached and separated shock/boundary-layer interaction cases. The shock function is also used to propose a robust form of the existing shock-unsteadiness model that simplifies the numerical implementation enormously.

Effects of the equivalence ratio on turbulent flame–shock interactions in a confined space

In this work, the influences of the equivalence ratio on flame front propagation velocity, shock wave velocity and pressure oscillation as well as flame–shock interactions with different combustion phenomena were comprehensively studied experimentally in a newly designed constant volume combustion bomb (CVCB). And a hydrogen–air mixture was chosen as the test fuel. In the CVCB, an orifice plate was used to obtain flame acceleration and promote turbulent flame formation. High-speed Schlieren photography was employed to capture the turbulent flame front and shock wave in the present work. The evolution of the flame and shock wave together with influences of the equivalence ratio on the flame tip velocity, shock wave velocity and pressure oscillation were clearly presented. The results showed that, after the laminar flame passed through the orifice plate, wrinkled turbulent flame gradually formed, and the shock wave ahead of flame front could be seen at a certain condition. The shock wave formation and enhancement process induced by flame acceleration was clearly captured by the Schlieren photography. It was found that the mean turbulent flame tip velocity reached a maximum value at an equivalence ratio of 1.25. In addition, an increase in the initial ambient pressure resulted in an increase of the turbulent flame tip velocity. Forced by the flame–shock/acoustic interactions, the flame would reverse and the backward flame velocity was positively related to that of the forward flame. The forward shock wave showed little differences among different equivalence ratios, while the reflected shock decayed fastest for the fastest flame, and the turbulent flame was pushed back more apparently. And the effect of the equivalence ratio on the pressure oscillation caused by flame acceleration and flame–shock interactions in the end gas region of confined space was determined.

Further improvement of weighted compact nonlinear scheme using compact nonlinear interpolation

To further improve the resolution of weighted compact nonlinear schemes(WCNS), a new 7th-order compact nonlinear interpolation method is proposed on the same stencil as 5th-order CRWENO scheme. Proper nonlinear weights are developed based on the Y type nonlinear weights, the properties of which are further analyzed in this paper. It is found that the Y type nonlinear weights are equivalent to the original nonlinear weights with an adaptive ϵ, which has very small value near discontinuities and very large value in smooth regions. As a result, the new nonlinear scheme has good shock capturing ability and achieves optimal order of accuracy in smooth regions. A new characteristic projection method is put forward, which largely reduces the computation costs. Simulations of Lax problem, Osher-Shu problem, double Mach reflection problem, decay of homogenous turbulence, shock turbulence interaction and turbulent channel flow show that the new scheme captures shocks without obvious oscillations, has higher resolution than other schemes tested, has obvious advantage in distinguishing turbulence from shocks and has higher efficiency.

Numerical analysis of shock wave and supersonic turbulent boundary interaction between adiabatic and cold walls

ABSTRACTDirect numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a 24° compression ramp with adiabatic and cold-wall temperatures are conducted. The wall temperature effects on turbulence structures and shock motions are investigated. The results are validated against previous experimental and numerical data. The effects of wall cooling on boundary layer characteristics are analysed. Statistical data show that wall cooling has a significant effect on the logarithmic region of mean velocity profile downstream the interaction region. Moreover, the influence of wall temperature on Reynolds stress anisotropy is mainly limited in the near-wall region and has little change on the outer layer. As the wall temperature decreases, the streamwise coherency of streaks increases. Based on the analysis of instantaneous Lamb vector divergence, the momentum transport between small-scale vortices on cold-wall condition is significantly enhanced. In addition, spectral analysis of wall pressure signals indicates that the location of peak of low-frequency energy shifts toward higher frequencies in cold case. Furthermore, the dynamic mode decomposition results reveal two characteristic modes, namely a low-frequency mode exhibiting the breathing motion of separation bubble and a high-frequency mode associated with the propagation of instability waves above separation bubble. The shape of dynamic modes is not sensitive to wall temperature.

A self-consistent analytical model for the upstream magnetic-field and ion-beam properties in Weibel-mediated collisionless shocks

A theoretical and numerical analysis is carried out for turbulent collisionless shocks mediated by the ion-Weibel instability during high-velocity plasma collisions. We develop a simple model based on the coalescence dynamics of the ion current filaments, which predicts the spatio-temporal evolution of the magnetic fluctuations formed in the upstream plasma region. From comparison with particle-in-cell simulations, our model is shown to correctly capture the magnetic-field and ion-beam properties during the early-time shock propagation.

Different combustion modes caused by flame-shock interactions in a confined chamber with a perforated plate

The present work investigates the interaction of the turbulent flame and shock wave as well as the end-gas autoignition in a newly designed constant volume combustion chamber equipped with a perforated plate using a stoichiometric hydrogen-air mixture. Detailed high speed schlieren photography is used to track the turbulent flame fronts and shock waves which are generated by the laminar flame passing through the perforated plate. The different propagation speeds of the turbulent flames and shock waves can be obtained by controlling the initial pressures and the hole size of the perforated plate. In this work, three combustion modes were obtained clearly by experiment, depending on the interactions of the turbulent flame and shock wave, such as normal combustion, oscillating combustion and end-gas autoignition. The normal combustion is a weak turbulent flame propagation without an obvious shock wave in the confined chamber. The oscillating flame propagation is generated by the interaction of the reflected shock wave and flame front and this process can be clearly visualized in the present work. The end-gas autoignition is induced by the combined effect of the supersonic flame and the shock waves. The accelerating combustion in the confined chamber could produce the primary shock wave and the subsequent secondary shock wave is induced by the secondary flame occurring between the primary flame and primary shock wave. It is found that the secondary shock wave with speed of 780m/s is faster than the primary one, which is the source of the end-gas autoignition. It is also observed that quasi-detonation wave produced by the end-gas autoignition can reach the speed of 1700m/s. This wave is accompanied by a strong pressure oscillation which can explain the mechanism of engine knock.

Intentional utilization of strong nonlinearity in structural dynamics

Given that the conventional view in engineering design is to regard nonlinearity as either unwanted or detrimental–a “nuisance” to be at most tolerated and “designed around”–or as a mere perturbation of the predominantly linear dynamics, the two standard approaches of nonlinear structural dynamics were developed: The linearized and weakly nonlinear approaches. Yet, recent work has revealed the important benefits that strong nonlinearity offers over broad areas, from turbulent flows, fluid-structure interactions, vibration and shock isolation, and acoustic metamaterials, to energy harvesting, blast and acoustic mitigation, and nano/micro design. Indeed, it is the author’s view that accounting for, understanding of, and designing with strong nonlinearity will become a cornerstone of future engineering practice. This work focuses on constructive utilization of intentional strong nonlinearity to enable passive energy management in dynamical systems across spatial and temporal scales. After a brief review of recent applications, emphasis is given to passive blast mitigation of large-scale infrastructure.

Learning partial differential equations via data discovery and sparse optimization.

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Large-eddy simulation of a pulsed jet into a supersonic crossflow

Abstract Numerical investigation of a pulsed jet injected into a supersonic crossflow was carried out using large-eddy simulation. The corresponding steady jet injection was also calculated for comparison with the pulsed jet injection and for validation against experimental data. Various fundamental mechanisms dictating the intricate flow characteristics, such as multi-scale vortical structures, complex shock systems, mixing properties and turbulence behaviors, have been studied. As the pulsed jet issuing transversely into the supersonic crossflow, the salient shock systems and vortical structures in terms of the instantaneous and phase-averaged flow field are analyzed. The large-scale jet shear vortices are formed along the interface of jet and crossflow due to the pulsation effect, which can promote the engulfing of the crossflow fluid and the mixing of the jet and crossflow fluids. Further we investigate turbulence properties of the jet and crossflow interaction and scalar statistics of the injectant mass fraction to reveal jet penetration enhancement and mixing property improvement for the pulsed jet. Results obtained in this study provide physical insight into the understanding the mechanisms for the interaction of pulsed jet and supersonic crossflow.

Intense laser driven collision-less shock and ion acceleration in magnetized plasmas

The generation of strong magnetic field with a laser driven coil has been demonstrated by many experiments. It is applicable to the magnetized fast ignition (MFI), the collision-less shock in the astrophysics and the ion shock acceleration. In this paper, the longitudinal magnetic field effect on the shock wave driven by the radiation pressure of an intense short pulse laser is investigated by theory and simulations. The transition of a laminar shock (electro static shock) to the turbulent shock (electromagnetic shock) occurs, when the external magnetic field is applied in near relativistic cut-off density plasmas. This transition leads to the enhancement of conversion of the laser energy into high energy ions. The enhancement of the conversion efficiency is important for the ion driven fast ignition and the laser driven neutron source. It is found that the total number of ions reflected by the shock increases by six time when the magnetic field is applied.

Constructal design of the mixing zone inside a supersonic ejector

Supersonic ejectors can be used in heat powered chillers to transfer mechanical energy between the motive and the inverse cycle. Within the ejector, momentum is exchanged between a high speed flow produced by a primary nozzle and a slow current coming from the chiller evaporator. Due to the supersonic regime of the primary flow, the mixing of the two streams causes significant loss and impairs the system efficiency. Up to now, second law efficiency of ejector chillers is quite low and optimization is highly needed. The fluid dynamics of the whole ejector involves turbulent mixing, shock trains and complex wall flow, requiring CFD analyses for an adequate description. However, in order to attempt an optimization, mathematically workable models are advantageous. An analytical scheme that captures the basic features of the turbulent mixing zone is discussed here in view of a Constructal design of an ejector chiller.

Simulation of shock–turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence

The one-dimensional turbulence (ODT) methodology is extended to include an efficient compressible implementation and a model for capturing shock-induced turbulence is presented. Lignell et al. recently introduced a Lagrangian ODT implementation using an adaptive mesh. As the code operates in the incompressible regime (apart from constant-pressure dilatation) it cannot handle compressibility effects and their interactions with turbulence and chemistry. The necessary algorithmic changes to include compressibility effects are highlighted and our model for capturing shock–turbulence interaction is presented. To validate our compressible solver, we compare results for the Sod shock tube problem against a finite volume Riemann solver. To validate our model for shock–turbulence interaction, we present comparisons for a non-reactive and a reactive case. First, results of a shock traveling from light (air) to heavy (SF6) with reshock have been simulated to match mixing width growth data of experiments and turbulent kinetic energy results from LES. Then, for one-step chemistry calibrated to represent an acetylene/air mixture we simulate the interaction of a shock wave with an expanding flame front, and compare results with 2D simulation (2D-sim) data for flame brush formation and ensuing deflagration-to-detonation transitions (DDT). Results for the Sod shock tube comparison show that the shock speed and profile are captured accurately. Results for the non-reactive shock–reshock problem show that interface growth at all simulated Mach numbers is captured accurately and that the turbulent kinetic energy agrees in order of magnitude with LES data. The reactive shock tube results show that the flame brush thickness compares well to 2D-sim data and that the approximate location and timing of the DDT can be captured. The known sensitivity of DDT characteristics to details of individual flow realizations, seen also in ODT, implies that model agreement can be quantified only by comparing flow ensembles, which are presently unavailable other than in an ODT run-to-run sensitivity study that is reported herein.

Simulations of Cellular Detonation Interaction with Turbulent Flows

Comparative studies of different inflow turbulent forcing effects on detonation front dynamics and the flow statistics are conducted through direct numerical simulations of turbulence–detonation/shock interactions. High-resolution bandwidth-optimized weighted essentially nonoscillatory scheme of spatial discretization and total variation diminishing temporal integration are used to solve the three-dimensional chemically reactive Navier–Stokes equations. The turbulent inflow vertical and entropic forcing effects on the three-dimensional detonation front and cellular structures are first analyzed. The influence of the inflow forcing on the generated regular cell patterns with diamond shape is compared. The vortex behind the detonation is quite different from that behind shock waves with the same inflow fluctuations. This also results in the larger increase of velocity variances downstream of detonation than the turbulence–shock case. The similar trend can also be found for the Taylor microscales. Effects of different inflow turbulence intensities are investigated. The irregular cellular detonations under vertical inflow forcing are also analyzed.

THE SCALING RELATIONS AND THE FUNDAMENTAL PLANE FOR RADIO HALOS AND RELICS OF GALAXY CLUSTERS

Diffuse radio emission in galaxy clusters is known to be related to cluster mass and cluster dynamical state. We collect the observed fluxes of radio halos, relics, and mini-halos for a sample of galaxy clusters from the literature, and calculate their radio powers. We then obtain the values of cluster mass or mass proxies from previous observations, and also obtain the various dynamical parameters of these galaxy clusters from optical and X-ray data. The radio powers of relics, halos, and mini-halos are correlated with the cluster masses or mass proxies, as found by previous authors, while the correlations concerning giant radio halos are in general the strongest. We found that the inclusion of dynamical parameters as the third dimension can significantly reduce the data scatter for the scaling relations, especially for radio halos. We therefore conclude that the substructures in X-ray images of galaxy clusters and the irregular distributions of optical brightness of member galaxies can be used to quantitatively characterize the shock waves and turbulence in the intracluster medium responsible for re-accelerating particles to generate the observed diffuse radio emission. The power of radio halos and relics is correlated with cluster mass proxies and dynamical parameters in the form of a fundamental plane.

Development and evaluation of anti-malarial bio-conjugates: artesunate-loaded nanoerythrosomes.

Biodegradable cellular carrier has desired properties for achieving effective long-term controlled release of drugs having short half life. To reduce the undesired effects of drug, advanced drug delivery systems are needed which are based on specific cell targeting module. Artesunate (ART) conjugation on nanoerythrosomes (NE) can have controlled delivery to avoid drug leakage, increase the stability, and reduce cost and toxicities. In this study nanosized lipoprotein membrane vesicles bearing ART were prepared by extrusion method. Developed ART-NE conjugate formulations were optimized on the basis of vesicle morphology, size and size distribution, polydispersity index, integrity of membrane, loaded drug concentration, drug leakage, effect of temperature and viscosity, syringeability, in vitro release profile and in vivo plasma concentration estimation studies. Fourier transform infrared (FTIR) spectroscopy reveals that lipid chain order of RBCs are insignificantly affected in moderate conditions after ART loading. The formulated ART-NE carrier revealed non aggregated, uniformly sized particles with smooth surfaces. The maximum drug loading was found to be 25.20 ± 1.3 μg/ml. ART-NE formulation was best fit for zero order kinetics and was found to be capable of controlled release of drug for 8 hrs. ART-NE formulation showed good redispersibility with desirable properties for parenteral administration. Formulation was stable when subjected to stress by centrifugal force of 7500 rpm and could bear turbulence shock of 15 passes from hypodermic needle of size 23 gauges. The ART-NE formulation administered intravenously showed higher plasma concentration compared to free drug signifying not only controlled release but higher rate of in vivo release. The developed formulation exhibited zero order release profile as per kinetic study analysis suggesting the suitability of carrier for the sustained and targeted delivery of ART. The developed ART-NE drug delivery system offers improved pharmacokinetic profile with assurance of increased therapeutic efficacy.

Vorticity dynamics after the shock–turbulence interaction

The interaction of a shock wave with quasi-vortical isotropic turbulence (IT) represents a basic problem for studying some of the phenomena associated with high speed flows, such as hypersonic flight, supersonic combustion and Inertial Confinement Fusion (ICF). In general, in practical applications, the shock width is much smaller than the turbulence scales and the upstream turbulent Mach number is modest. In this case, recent high resolution shock-resolved Direct Numerical Simulations (DNS) (Ryu and Livescu, J Fluid Mech 756:R1, 2014) show that the interaction can be described by the Linear Interaction Approximation (LIA). Using LIA to alleviate the need to resolve the shock, DNS post-shock data can be generated at much higher Reynolds numbers than previously possible. Here, such results with Taylor Reynolds number approximately 180 are used to investigate the changes in the vortical structure as a function of the shock Mach number, $$M_{s}$$ , up to $$M_{s}=10$$ . It is shown that, as $$M_{s}$$ increases, the shock interaction induces a tendency towards a local axisymmetric state perpendicular to the shock front, which has a profound influence on the vortex-stretching mechanism and divergence of the Lamb vector and, ultimately, on the flow evolution away from the shock.

A space–time adaptive discontinuous Galerkin scheme

A discontinuous Galerkin scheme for unsteady fluid flows is described that allows a very high level of adaptive control in the space–time domain. The scheme is based on an explicit space–time predictor, which operates locally and takes the time evolution of the data within the grid cell into account. The predictor establishes a local space–time approximate solution in a whole space–time grid cell. This enables a time-consistent local time-stepping, by which the approximate solution is advanced in time in every grid cell with its own time step, only restricted by the local explicit stability condition. The coupling of the grid cells is solely accomplished by the corrector which is determined by the numerical fluxes. The considered discontinuous Galerkin scheme allows non-conforming meshes, together with p-adaptivity in 3 dimensions and h/p-adaptivity in 2 dimensions. Hence, we combine in this scheme all the flexibility that the discontinuous Galerkin approach provides. In this work, we investigate the combination of the local time-stepping with h- and p-adaptivity. Complex unsteady flow problems are presented to demonstrate the advantages of such an adaptive framework for simulations with strongly varying resolution requirements, e.g. shock waves, boundary layers or turbulence.

HOT GASEOUS ATMOSPHERES IN GALAXY GROUPS AND CLUSTERS ARE BOTH HEATED AND COOLED BY X-RAY CAVITIES

Expanding X-ray cavities observed in hot gas atmospheres of many galaxy groups and clusters generate shock waves and turbulence that are primary heating mechanisms required to avoid uninhibited radiatively cooling flows which are not observed. However, we show here that the evolution of buoyant cavities also stimulates radiative cooling of observable masses of low-temperature gas. During their early evolution, radiative cooling occurs in the wakes of buoyant cavities in two locations: in thin radial filaments parallel to the buoyant velocity and more broadly in gas compressed beneath rising cavities. Radiation from these sustained compressions removes entropy from the hot gas. Gas experiencing the largest entropy loss cools first, followed by gas with progressively less entropy loss. Most cooling occurs at late times, $\sim 10^8-10^9$ yrs, long after the X-ray cavities have disrupted and are impossible to detect. During these late times, slightly denser low entropy gas sinks slowly toward the centers of the hot atmospheres where it cools intermittently, forming clouds near the cluster center. Single cavities of energy $10^{57}-10^{58}$ ergs in the atmosphere of the NGC 5044 group create $10^8 - 10^9$ $M_{\odot}$ of cooled gas, exceeding the mass of extended molecular gas currently observed in that group. The cooled gas clouds we compute share many attributes with molecular clouds recently observed in NGC 5044 with ALMA: self-gravitationally unbound, dust-free, quasi-randomly distributed within a few kpc around the group center.