Strength Of Incident Shock Wave Research Articles

Analysis of wave converging phenomena inside the shocked two-dimensional cylindrical water column

Due to the curvature of the droplet surface, the propagation of transmitted waves is complex inside a droplet impacted by an incident shock wave. The wave converging phenomena inside a two-dimensional water column impacted by different curved shock waves are explored in this paper by means of theoretical ray analysis and high-resolution numerical simulations. An analytical method describing the wave structure evolution characteristics inside the shocked water column is established. Hence, the morphological pattern and focus locations of these waves are theoretically obtained. The analysis shows that both the first and the second reflected waves focus inside the water column regardless of the convergent, planar or divergent nature of the incident shock wave shape. The dimensionless distances from focusing points to the column centre are derived as ${\kappa }/{( 3\kappa -{{M}_{0}}{{f}_{s}} )}$ for the former and ${\kappa }/{( 5\kappa -{{M}_{0}}{{f}_{s}})}$ for the latter, respectively. Here, $\kappa$ , $M_0$ and $f_s$ represent the sound-speed ratio of the two phases, the incident shock wave strength and a function characterising the shock wave shape effect, respectively. Moreover, highly negative pressures due to the first reflected wave focusing and significant pressure oscillations due to the second reflected wave focusing are numerically tracked for three shapes of the incident shock. The effects of the incident shock wave intensity on the pressure variations at focus points are further studied. As the incident shock wave intensity increases, stronger negative pressure and higher pressure oscillation are induced. The converged incident shock wave can enhance the above phenomena, but the diverged one can weaken them.

Numerical study of three-dimensional developments of premixed flame induced by multiple shock waves

The three-dimensional interactions of a perturbed premixed flame interface with a planar incident shock wave and its reflected shock waves are numerically simulated by solving the compressible, reactive Navier–Stokes equations with the high-resolution scheme and a single-step chemical reaction. The effects of the initial incident shock wave strength (Mach number) and the initial perturbation pattern of interface on the interactions are investigated. The distinct properties of perturbation growth on the flame interface during the interactions are presented. Our results show that perturbation growth is mainly attributed to the flame stretching and propagation. The flame stretching is associated with the larger-scale vortical flow due to Richtmyer–Meshkov instability while the flame propagation is due to the chemical reaction. The mixing properties of unburned/burned gases on both sides of the flame are quantitatively analyzed by using integral and statistical diagnostics. The results show that the large-scale flow due to the vortical motion always plays a dominating role during the reactive interaction process; however, the effect of chemistry becomes more important at the later stage of the interactions, especially for higher Mach number cases. The scalar dissipation due to the molecular diffusion is always small in the present study and can be negligible.

Influences of Inlet Geometry Modification on Scramjet Flow and Combustion Dynamics

The influences of inlet geometry modification on flow and combustion dynamics are experimentally investigated in a model supersonic combustion ramjet (scramjet) installed in Mach 4.5 high-enthalpy air freestreams. The inlet upper-lip angle (6, 12, and 20 deg) and the intake contraction ratio (1.3 and 1.9) chosen as the generic inlet design parameters are varied. With the inlet geometries systematically modified, flowfields inside the model scramjet are visualized at cold conditions (room temperature) using a planar laser Rayleigh scattering method (wherein laser radiation is scattered by carbon dioxide particles). In addition, combustion dynamics and structures in the scramjet combustor are investigated in high-enthalpy flows with a total temperature of 2600 K capable of autoigniting injected fuels. High-frame-rate time-averaged chemiluminescence (broadband) imaging and hydroxyl planar laser-induced fluorescence are used for this investigation. Incident shock-wave strength, separated flow behavior, boundary-layer development, combustion structure/anchoring, and chemiluminescence intensity are found to be sensitive to the inlet geometry modifications.

A parameterization of the Richtmyer–Meshkov instability on a premixed flame interface induced by the successive passages of shock waves

The interactions of a sinusoidal premixed flame interface with successive shock waves are studied by numerically solving the two-dimensional, reactive Navier–Stokes equations with high resolution schemes. The focus is the development of the perturbations on the flame interface due to the Richtmyer–Meshkov (RM) instability. A single irreversible chemical reaction for a C2H4+3O2+4N2 mixture is used to represent the combustion process during the interactions. Three cases of interactions, with different initial incident shock wave strengths (Ma=1.2, 1.7 and 2.2), are studied. The multiple interactions between the flame interface and the shock and its reflection waves lead to interesting new observations that have not been presented before. To parameterize the interactions, we introduce a time scale decoupling assumption, and propose to use two decoupled time scales, i.e., the decoupled chemical reaction time scale τC and the decoupled RM instability time scale τRM. Based on this assumption, τC is considered to be decoupled from τRM, so that both time scales can be defined and determined independently. Specifically, τRM is defined as the reciprocal of vorticity magnitudes that can be obtained by performing the computations of two-dimensional RM instability in a chemically frozen flow that removes the effect of chemical reactions. On the other hand, τC is defined as the ratio of reaction zone width of an un-stretched, laminar, premixed flame to propagating speed of the flame, during the one-dimensional laminar flame propagation without considering two-dimensional RM instability. Using these definitions, our calculations show that both τC and τRM decrease with the successive interactions of the shock waves with the flame interface in all three cases, and that τC is larger than τRM at early stages of interactions and then rapidly decreases to a level comparable with τRM at later stages of interactions. We compare the two-dimensional visualizations of the perturbation development on the interface in reactive flows with those in chemically frozen flows. The comparison shows that RM instability plays an important role in early evolution, but chemical reactions dominate later, and that the evolution is correlated with the variations of τC and τRM for all cases studied here. The quantitative correlations between the ratio of τC to τRM and chemical heat release rate in all three cases are calculated. The good correlations indicate the advantage of the approaches to determine τC and τRM proposed in present study. The observation that the ratio of τC to τRM is independent of the initial strength of incident shock wave suggests that the ratio reflects the nature of reactive RM instability, hence provides a new dimensionless parameter for understanding such flows.

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma = 1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma = 2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.

Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave

The effect of incident shock wave strength on the decay of interface introduced perturbations in the refracted shock wave was studied by performing 20 different simulations with varying incident shock wave Mach numbers (M ~ 1.1− 3.5). The analysis showed that the amplitude decay can be represented as a power law model shown in Eq.7, where A is the average amplitude of perturbations (cm), B is the base constant (cm−(E−1), S is the distance travelled by the refracted shockwave (cm), and E is the power constant. The proposed model fits the data well for low incident Mach numbers, while at higher mach numbers the presence of large and irregular late time oscillations of the perturbation amplitude makes it hard for the power law to fit as effectively. When the coefficients from the power law decay model are plotted versus Mach number, a distinct transition region can be seen. This region is likely to result from the transition of the post-shock heavy gas velocity from subsonic to supersonic range in the lab frame. This region separates the data into a high and low Mach number region. Correlations for the power law coefficients to the incident shock Mach number are reported for the high and low Mach number regions. It is shown that perturbations in the refracted shock wave persist even at late times for high incident Mach numbers.

気泡を含む液体中を伝播する衝撃波現象に関する研究(S26-4 高速流れと衝撃波現象の基礎と応用その4,S26 高速流れと衝撃波現象の基礎と応用)

Shock wave propagation and collapse of gas bubbles caused by a shock in a water containing gas bubbles are of large interest in relation to characteristics of water hammer, blowdown of high pressure liquids in pipes, etc. The large-amplitude shock wave propagations in the bubbly liquids are investigated using a two-phase shock tube. Effects of incident shock wave strength on shock wave pressure characteristics are clarified. Behavior of the bubbles collapsing behind large-amplitude shock waves is also clarified by pressure history measurements and high speed photography.

Aluminum dust ignition behind reflected shock wave: two-dimensional simulations

In this paper results of parallel computer simulations on aluminum dust ignition behind a reflected shock wave are presented. Computations show the time-evolution of a complicated flow field created due to a shock wave collision with a pile of dust, shock reflection from a wall, and its interaction with vortices. Particles, blown away by the incident shock, are heated mainly behind the reflected shock wave. The estimated ignition delay time is of the order of 80–100 μs and is a strong function of the incident shock wave strength. The simulations show that it may be very difficult to ignite aluminum particles when the incident shock wave Mach number is smaller than about Ms ≈ 3, while for stronger shocks the estimated ignition delay time quickly decreases.

Large-Amplitude Shock Wave Propagation and Bubble Collapse in a Water Containing Gas Bubbles.

Shock wave propagation and collapse of gas bubbles caused by a shock in a water containing gas bubbles are of large interest in relation to characteristics of water hammer, blowdown of high pressure liquids in pipes, damping of dynamic influence of shock waves on obstacles, etc. The large-amplitude shock wave propagations in the bubbly liquid are investigated using a two-phase shock tube. Effects of incident shock wave strength and initial void fraction on shock wave pressure characteristics are clarified for incident shock wave strength ranging from 0.06 MPa to 0.25 MPa. Behavior of the bubbles collapsing behind large-amplitude shock waves is also clarified by pressure history measurements and high speed photography.

205 気泡流中の強い衝撃波現象に関する研究

The large-amplitude shock wave propagation phenomena in air-bubbles/water mixtures were investigated using a two-phase shock tube. Effect of incident shock wave strength on shock wave pressure characteristics in mixtures and the precursor of shock wave are analyzed. It was found that the large-amplitude shock waves have high-frequency oscillation components and the precursor.