Shock Rise Time Research Articles

State of the art of sonic boom modeling

The fundamentals of sonic boom theory were established and validated in the 1950s and early 1960s. By the early 1970s, these were implemented into practical models. Over the past decade, there have been requirements for design tools for an advanced supersonic transport and environmental assessment of launch vehicles and military aircraft operations. This has resulted in a number of advances in the understanding of sonic boom shock rise times, propagation through turbulence, use of computational fluid dynamics in sonic boom modeling, and analysis of launch vehicle sonic boom including the effect of large underexpanded rocket plumes. This paper reviews the early established theory, the recent advances in theory, and the application of these advances to practical models.

Optimal and wavelet-based shock wave detection and estimation

Detection and estimation of aeroacoustic shock waves generated by supersonic projectiles are considered. The shock wave is an N-shaped acoustic wave emanating in the form of an acoustic cone trailing the projectile. An optimal detection/estimation scheme is considered based on a parametric signal plus white Gaussian noise model. To gain robustness and reduce complexity, we then focus on gradient estimators for shock wave edge detection, exploiting the very fast shock rise and fall times. The approach is cast in terms of a wavelet transform where the level of smoothing corresponds to scale. A multiscale analysis is described, consisting of multiscale products, to enhance edge detection and estimation. This method is effective and robust with respect to unknown environmental interference that will generally not exhibit singularities as sharp as the N-wave edges. Experimental results are presented for discriminating N waves in the presence of vehicle noise. Results are also shown, as a function of miss distance, for gradient-based detection of simulated small projectile shocks inserted into recorded tank noise.

Experimental characterization of quasi static and shock wave behavior of porous aluminum

Experiments of quasi static hydrostatic and uniaxial strain compression, and of shock wave propagation performed on 9% and 17% porous aluminum are presented, analyzed, and compared. Quasi static experiments show the influence of coupling between void collapse and plasticity induced in the matrix on the material macroscopic behavior. The amount of pore compaction appears to be enhanced by the deviatoric stress component present in the uniaxial strain tests and not in the hydrostatic ones. The originality of the plate impact setup and its associated metrology [velocity interferometer system for any reflector (VISAR) interferometry and polyvinylidene fluoride (PVDF) piezoelectric gages] exhibits also the influence of these local physical mechanisms on shock wave propagation in porous aluminum. More, the variations observed between the rise times of shocks seem to point out a preponderance of the dynamic effects (inertia or strain rate) over the material behavior. We observe indeed that the higher the stress in the material, the shorter the shock rise time. This point is confirmed by comparing quasi static and dynamic responses of porous aluminum. Comparison of these experimental results to numerical simulations should be interesting to prove or not this hypothesis.

In Vivo Pressure Measurements of Lithotripsy Shock Waves in Pigs

Stone comminution and tissue damage in lithotripsy are sensitive to the acoustic field within the kidney, yet knowledge of shock waves in vivo is limited. We have made measurements of lithotripsy shock waves inside pigs with small hydrophones constructed of a 25-μm PVDF membrane stretched over a 21-mm diameter ring. A thin layer of silicone rubber was used to isolate the membrane electrically from pig fluid. A hydrophone was positioned around the pig kidney following a flank incision. Hydrophones were placed on either the anterior (shock wave entrance) or the posterior (shock wave exit) surface of the left kidney. Fluoroscopic imaging was used to orient the hydrophone perpendicular to the shock wave. For each pig, the voltage settings (12–24 kV) and the position of the shock wave focus within the kidney were varied. Waveforms measured within the pig had a shape very similar to those measured in water, but the peak pressure was about 70% of that in water. The focal region in vivo was 82 mm × 20 mm, larger than that measured in vitro (57 mm × 12 mm). It appeared that a combination of nonlinear effects and inhomogeneities in the tissue broadened the focus of the lithotripter. The shock rise time was on the order of 100 ns, substantially more than the rise time measured in water, and was attributed to higher absorption in tissue.

Ultrafast Raman Spectroscopy of Shock Fronts in Molecular Solids

The passage of a 4 GPa shock front through an embedded optical nanogauge, a thin ({approximately}700 nm) layer of polycrystalline molecular material (anthracene), is monitored in real time by picosecond coherent Raman scattering. Analysis of high resolution Raman spectra shows the shock rise time is less than 25ps, and the front is less than 100 molecules wide. The rise time is faster than relaxation of nonequilibrium populations of molecular vibrations, which shows a shock front in a molecular material can leave highly nonequilibrium vibrational states in its wake. The implications for shock initiation of energetic materials, typically polycrystalline molecular solids, are briefly discussed. {copyright} {ital 1997} {ital The American Physical Society}

In vivo measurements of lithotripsy shock waves in pigs

Mechanisms of stone comminution and tissue damage in lithotripsy are sensitive to the acoustic field within the kidney, yet prediction of shock wavesin vivo is difficult. Measurements of lithotripsy shock waves have been made inside pigs with small hydrophones constructed of a 50-μm PVdF membrane stretched over a 21-mm-diam ring. A thin layer of silicone rubber was used to electrically isolate the membrane from pig fluid. An incision was made in the pig flank and a hydrophone inserted either on the anterior (shock wave entrance) or posterior (shock wave exit) surface of the left kidney. The incision was flooded with saline during closure to minimize entrapped air. Four pigs were treated in a Dornier HM-3 lithotripter. Fluoroscopic imaging was used to orient the hydrophone perpendicular to the shock wave. For each pig, various power settings and movement of the shock wave focus throughout the kidney were used. Waveforms measured within the pig had a shape very similar to those measured in water. However, pressure amplitude in the pig was about 60% of that measured in water. The shock rise times were on the order of 100 μs and were hydrophone limited. [Work supported by NIH and the ASA Hunt Fellowship.]

Particle-level modeling of dynamic consolidation of Ti-SiC powders

Shock wave processing of Ti-SiC powders has been numerically analyzed at the particle level using an Eulerian finite-element methodology. The analysis reveals that the shock consolidation is dominated by the viscoplastic deformation of Ti particles and that inertia plays a significant role in setting the magnitude of the shock rise time (i.e. the consolidation time). The addition of SiC particles is found to reduce slightly the degree of the localized deformation and the temperature rise around the Ti particle surfaces (the hot spots). The local temperature distribution and the thermal history of the hot spots from the simulation are found to be useful in estimating the initiation and growth of the interfacial reaction layer between Ti and SiC. The final particle packing configuration of Ti/SiC powder mixtures and the Ti-SiC reaction layer thickness predicted by the simulations are found to be consistent with experimental observations. Our study indicates that a combination of shock wave processing of powders by plate impact experiments with soft recovery capabilities and the accompanying numerical simulation of these experiments at the particle level holds promise for understanding thermal-mechanical mechanisms during shock consolidation of reactive powders.

Rise time in shock consolidation of materials

The rise time of a strong shock wave propagating through a porous material is estimated by analyzing the finite deformation of an elastic/viscoplastic spherical shell under impulsive pressure loading. The analysis examines explicitly the effects of dynamic loading rate and initial temperature and explains the relatively large shock rise times observed in porous materials. Results of the analysis provide a consistent and realistic interpretation of available experimental data.

Flight test measurements of the effect of turbulence on sonic boom peak overpressure and rise time

Sonic boom bow shock amplitude and rise time statistics from a sonic boom propagation flight test experiment are presented. The experiment consisted of flying two types of aircraft, the T-38 and F-15, at speeds of Mach 1.2 to 1.3 over a ground-based microphone array with concurrent meteorological measurements. Bow shock overpressure and rise time distributions measured under low and moderate atmospheric turbulence conditions for the same test aircraft are quite different. The peak overpressure distributions are skewed positively, indicating a tendency toward positive deviations from the mean. Standard deviations of overpressure distributions measured under moderate turbulence were slightly larger than those measured under low turbulence. Under moderate turbulence conditions the mean rise time was larger by a factor of 3.7 and the standard deviation was larger by a factor of 3.2 from the low turbulence values. These changes resulted in a transition from a peaked appearance of the low-turbulence rise time distribution to a flattened appearance for moderate turbulence rise time distributions.

The effect of turbulence on the loudness of sonic booms

Turbulence is known to distort sonic booms in two ways: random perturbations occur at and following each shock, and the shock rise time increases. Both types of distortion affect the high-frequency content of a boom, and are therefore important to loudness. It is of particular interest whether this distortion will adversely affect the loudness of minimized sonic boom signatures that are associated with low-boom supersonic transport design. Available scattering theories for the magnitude of perturbations and for shock rise times were extended to provide estimates of the spectral content of the distortions. During this analysis, care was taken to recognize the interacting roles of turbulent scattering, absorption of sound by molecular relaxation, and weak nonlinear steepening. It was found that the perturbations at and following the shocks tend to increase the loudness, while the increased rise times tend to decrease the loudness by a comparable amount. Because turbulent scattering is random and three dimensional, an individual boom may be affected by one of these effects more than by the other. Turbulence can therefore cause significant variation in the loudness of individual booms. The change to the average loudness of a number of booms, which is primary to the assessment of cumulative community impact, will, however, be small. [Work supported by NASA−Langley Res. Ctr.]

The healing distance of steady-state shock waves in the atmosphere

The Anderson algorithm has been used to calculate the time development and rise time of transient shock waves in the atmosphere. This algorithm has been applied to square pulses in order to investigate the healing distance of steady-state shocks perturbed by turbulent scattering. Perturbed 100-Pa shocks require on the order of 1.0-km travel distance to return to within 10% of their steady shock rise time. For 30-Pa shocks the minimum recovery distance increases to 3.0 km. It is unlikely that finite wave effects can remove the longer rise times and irregular features introduced into the sonic boom by turbulent scattering in the planetary boundary layer.

A numerical model for the propagation of sonic booms through an inhomogeneous, windy atmosphere.

The ZEPHYRUS computer model has been developed to calculate sonic boom propagation through a realistic atmosphere. This model includes the effects of (1) nonlinear distortion (weak shock theory), (2) attenuation and dispersion due to thermoviscous effects and oxygen and nitrogen molecular relaxation, and (3) an inhomogeneous, stratified atmosphere with a stratified wind field. Propagation through reflections and weak (linelike) caustics are included. Analysis of the stability of shocks shows that the characteristic formation distance for stable shocks may be greater than previously believed. In general, stable shocks have not formed when the sonic boom reaches the ground. Also, the rise time has been demonstrated to have a strong dependence on the waveform shape immediately behind the lead shock. Investigations have revealed an interesting phenomenon in which the rise time displays a second peak at the midlevel altitudes, both before and after reflection. This is apparently due to the dispersion from oxygen molecular relaxation when the characteristic relaxation time closely matches the lead shock rise time. [Work supported by NASA and ARL-UT IR&D program.]

Performance of an electrohydraulic shock wave lithotripter measured with thin film PVDF transducers.

Measurements of the operation and performance of a research lithotripter have been carried out using a new thin film polyvinylidene fluoride (PVDF) pressure transducer. The research lithotripter is modeled after a commercial electrohydraulic machine. Experimental techniques to match nanosecond-response transducers to digital sampling oscilloscopes are described. Shock rise times at F2 of about 45 ns are measured. Techniques have been developed for characterizing lithotripter focal properties by a combination of remote measurement and calculation to minimize damage to transducers. The results of numerical calculations of focusing shock waves in water by the method of shock dynamics are presented. The measurements show that the strength of shock waves in electrohydraulic lithotripters varies from shot to shot by as much as 40%, even though the discharge current of the shock generator is repeatable. Thus every shot in experiments carried out with these machines should be monitored with a reference transducer. It is suggested that the variability is due to the large sensitivity of ellipsoid optics to small changes of the symmetry of the spark discharge. The effects of tissue phantoms on focusing shock waves are reported.

INFLUENCE OF LOADING PATHS ON THE MECHANICAL RESPONSE AND SUBSTRUCTURE EVOLUTION OF SHOCK-LOADED COPPER

Shock recovery experiments on copper have been conducted to investigate the influence of loading rate and stress amplitude on defect storage and post-shock mechanical properties. The shock risetimes varied approximately from one nanosecond for the shock experiments to one microsecond for quasi-isentropic loading experiments. All the experiments had the same peak pressure and pulse duration. Decreasing the strain-rate of loading is shown to increase both the defect storage and post-shock yield strength of copper. The effect of loading rate on post-shock substructure and mechanical response of impacted copper is postulated to be directly related to the amount of dislocation motion before interaction with other dislocations and to the amount of reversible dislocation motion and resultant annihilation during the rarefaction portion of the shock-release cycle. 10 refs., 5 figs.

Molecular relaxation is insufficient to explain the shock structure and rise times of sonic booms; turbulence is apparently important

The authors have been recently examining some sonic‐boom waveforms that were recorded during overflights by the Air Force and that have become available to NASA and its contractors. The quality of the digitized data and the supporting meteorological data was such that one could test the applicability of molecular relaxation theories. In the late sixties it had been supposed that the finite rise times of sonic booms was attributable to atmospheric turbulence, but it was later pointed out that the first estimates of rise times in the absence of turbulence had neglected the vibrational relaxation of nitrogen molecules. Bass et al. [J. Acoust. Soc. Am. 74, 1514–1517 (1983)] have demonstrated that molecular relaxation definitely gives the correct order of magnitude of the observed rise times. However, the Air Force data in conjunction with the recent steady‐state shock profile model theory of Kang and Pierce give the first opportunity to make a detailed quantitative assessment of the molecular relaxation hypothesis. The agreement of theory with experiment in some cases is remarkably excellent, but in the preponderance of cases the rise of the shock is slower and the rise time is longer, typically by factors of the order of 2 to 3. [Work supported by NASA‐LRC and by the William E. Leonhard endowment to Penn State Univ.]

Propagation of medium strength shock waves through the atmosphere

The rise times and overpressures for shock waves from supersonic projectiles have been measured under a variety of atmospheric conditions. These measurements extend the overpressure for which weak shock theory adequately predicts measured values to 3 kPa. Predicted shock rise times agree reasonably well with theory for shock overpressures between 0.04 and 0.5 kPa with differences increasing at higher overpressures. At overpressures greater than 0.5 kPa, measured rise times might be limited by the experimental apparatus. No correlation between measured rise times and atmospheric turbulence was observed.

The effect of temperature on viscoplastic pore collapse

The hollow-sphere model, with temperature-dependent viscoplastic material response, is used to investigate thermal effects in shock compaction of metal powders. Model calculations show very good agreement with experimental shock rise times only if the temperature dependence is considered. The results also suggest that the dynamic compaction may be qualitatively different depending on whether viscoplastic or inertial effects dominate the pore collapse process.

Long‐range nonlinear propagation of explosive waveforms in the ocean

The propagation of idealized model waveforms, representative of underwater explosions measured at moderate distances (particle Mach number ≃0.06), has been simulated numerically out to large distances in an idealized uniform ocean. Besides chemical relaxation, the calculation procedure includes nonlinear waveform distortion and thermoviscous dissipation at shocks; these nonlinear phenomena are described using the weak‐shock approximation. Results from the uncorrected weak‐shock model, which omits chemical relaxation effects, are known to deviate appreciably from long‐range measurements [P. H. Rogers, J. Acoust. Soc. Am. 62, 1412–1419 (1977)]; the discrepancy is explained by showing, with the aid of the present model, that initial waveforms having different time scales exhibit markedly different long‐range behaviors. Specific waveform properties examined include the peak pressure, decay time constant, positive‐phase impulse, and shock rise time. Reasonable agreement is demonstrated between model predictions and long‐range measurements in the ocean, as represented by empirical scaling laws. [Work supported in part by ONR.]

Energy deposition and microstructural modification in dynamically consolidated metal powders

A model is presented for the deposition of energy at powder particle surfaces during dynamic consolidation. The average energy flux incident on the surface of a powder particle is estimated to be E/τA where E is the specific energy deposited by the shock, τ is the shock rise time, and A the measured powder specific surface area. This flux is assumed to be constant over the rise time of the shock, falling abruptly to zero for times longer than τ. Solution of the thermal transport equation subject to this boundary condition yields the thermal history within a powder particle having the area-equivalent diameter 𝒟=6/ρ0A, where ρ0 is the solid density. The magnitude of the temperatures and the heating and cooling rates indicate likely material transformations. The penetration of a given isotherm provides an estimate of the volume fraction of material transformed. Good agreement is found between model calculations and measurements of the extent of local martensite formation in consolidated 4330V steel powder and of local melting in consolidated aluminum-6% silicon and copper powders. The general implications of the model are discussed.

Modeling Film Boiling Destabilization Due to a Pressure Shock Arrival

The phenomenon of film destabilization due to an externally applied pressure transient has been investigated experimentally by Inoue and Bankoff. This film collapse process is of interest with regard to vapor explosions. An important step in vapor explosions is believed to be the onset of the rapid heat transfer between the molten fuel and coolant caused by pressure-pulse-induced film boiling destabilization. A dynamic film boiling model was developed to analyze film destabilization, and to predict from Inoue's experiment over a range of initial pressures and final shock pressures, shock rise times, and heater surface temperatures. The model indicated three important results: The nonequilibrium model shows better quantitative agreement with the data while the equilibrium model generally underpredicts the peak heat flux q /SUB p/ by a factor of 2 to 3 for short shock rise times (/tau/ /SUB p/ approx. = 80 ..mu..s). Both models neglect the effect of interface distortions due to Taylor instabilities. This physical effect should increase the predicted values of the peak heat flux. The film collapse process can be successfully modeled using an equilibrium model for shock rise times > 100 ..mu..s and is in agreement with the nonequilibrium model. One possible inference from thismore » analysis is that the suppression of vapor explosions due to initial conditions (e.g., ambient pressure) is caused by the increasing difficulty of collapsing the vapor film. Thus, to overcome the effects of these initial conditions, a more energetic trigger needs to be applied to destabilize the film and to induce the explosion.« less