Shock Motion Research Articles

Detonation shock dynamics and comparisons with direct numerical simulation

Comparisons between direct numerical simulation (DNS) of detonation and detonation shock dynamics (DSD) is made. The theory of DSD defines the motion of the detonation shock in terms of the intrinsic geometry of the shock surface, in particular for condensed phase explosives the shock normal velocity, D n , the normal acceleration, [Ddot] n , and the total curvature, κ. In particular, the properties of three intrinsic front evolution laws are studied and compared. These are (i) constant speed detonation (Huygens construction), (ii) curvature-dependent speed propagation (κ relation) and (iii) curvature- and speed-dependent acceleration ([Ddot] n –D n –κ relation). We show that it is possible to measure shock dynamics directly from simulation of the reactive Euler equations and that subsequent numerical solution of the intrinsic partial differential equation for the shock motion (e.g. a [Ddot] n –D n –κ relation) reproduces the computed shock motion with high precision.

Analysis and simulation of a turbulent, compressible starting vortex

The numerical simulation of a shock induced, turbulent compressible vortex is analyzed. The vortex is generated by the movement of an (unsteady) shock over the trailing-edge of a two-dimensional airfoil at different incidence angle. A theoretical analysis is performed for the case of a turbulent line vortex, at a low (vortex) Mach number and high Reynolds number, as a basis of comparison for the dynamic structure of the starting vortex. This theoretical analysis confirms the existence of an equilibrium structure of the isolated vortex similar to the laminar case. In the numerical computations, both an isotropic eddy viscosity two-equation turbulence model and an algebraic stress model are employed to assess the influence of turbulence model on the predictive capabilities of such a flow including the realization of the self-similar behavior found in the isolated vortex case. The results are also compared to theoretical estimates of the production-to-dissipation rate ratio for both types of turbulence models, and to recent experiments on such flows.

Investigations of High-Speed Civil Transport Inlet Unstart at Angle of Attack

The unstart transient of a high-speed civil transport mixed compression axisymmetric inlet at Mach 2 and 2-deg angle of attack was investigated numerically by using a three-dimensional time-accurate Navier‐Stokes solver. The Baldwin ‐Lomax algebraic turbulence model and an extrapolation uniform mass bleed boundary condition for the slot bleed were employed. It is observed that, when an angle of attack is imposed, the e ow on the leeward side has a stronger compression than that at zero angle of attack. The strong compression reduces the Mach number upstream of the terminal shock and therefore makes the shock move upstream e rst on the leeward side. The initial shock motion starts with the bifurcation of the terminal shock. The lower part of the split shock is stable because of the centerbody bleed, whereas the top part of the shock continues to travel upstream. When the terminal shock on the leeward side passes the bleed region, a separation is induced by the shock /boundary-layer interaction on the shoulder of the inlet centerbody, and the entire inlet is brought to unstart. The overall computed e owe eld phenomena agree qualitatively with the experimental observations.

A magnetic cloud with unusual structure and corresponding bow shock movement observed on May 13, 1995

A magnetic cloud embedded in a corotating interaction region was observed by Wind 244 Re upstream of Earth on May 13, 1995. This cloud was unusual as it had at least two internal structures and the profile of the magnetic field strength was far from that predicted by a simple force‐free flux rope model, although the field direction fit well. About 90 min later, this cloud was detected by the IMP 8 and Geotail satellites in front of Earth's bow shock. Geotail observed a sunward movement of the bow shock 8 min after the passage of the front boundary. An earthward movement of the bow shock was observed about 3 hours later. From the normal vector of the bow shock front, we deduce that the shape of the expanding bow shock was distorted from an axially symmetric geometry. The shape was consistent with distortion due to the observed inclination of the front boundary of the magnetic cloud.

Improvements to a tightly coupled viscous–inviscid procedure for three-dimensional unsteady transonic flow

A tightly coupled procedure for solving three-dimensional compressible viscous flows has been developed. In this approach, the flow field is divided into two domains, a viscous domain surrounding viscous wakes and solid surfaces such as wings or rotor blades, and an outer domain where the inviscid, unsteady compressible potential flow equations hold. These two zones are tightly coupled to each other, allowing conservation of mass, momentum and energy at the interface, and permitting the propagation of non-linear acoustic waves from one zone to another in a seamless fashion. The location of the interface dividing the two zones is allowed to adjust its position relative to blade based on an investigation of the instantaneous flow physics. The effects of rotor trim, aeroelasticity, and far wake induced inflow are included in the analysis through a coupling with a comprehensive rotor analysis. The methodology has been applied to two cases which represent the flow physics typically encountered by modern helicopter rotors. A cruise condition for a UH-60 is analyzed and the results compared with both experimental data and full Navier–Stokes results. Computer time savings realized by the zonal method over the full Navier–Stokes analysis are given. A non-lifting high speed case is also investigated to assess the accuracy of unsteady shock motion. The shock structure is examined to determine whether inaccuracies are introduced by the presence of the interface.

Shock oscillation in underexpanded screeching jets

The periodic oscillation of the shock waves in screeching, underexpanded, supersonic jets, issuing from a choked, axisymmetric, nozzle at fully expanded Mach numbers (Mj) of 1.19 and 1.42, is studied experimentally and analytically. The experimental part uses schlieren photography and a new shock detection technique which depends on a recently observed phenomenon of laser light scattering by shock waves. A narrow laser beam is traversed from point to point in the flow field and the appearance of the scattered light is sensed by a photomultiplier tube (PMT). The time-averaged and phase-averaged statistics of the PMT data provide significant insight into the shock motion. It is found that the shocks move the most in the jet core and the least in the shear layer. This is opposite to the intuitive expectation of a larger-amplitude shock motion in the shear layer where organized vortices interact with the shock. The mode of shock motion is the same as that of the emitted screech tone. The instantaneous profiles of the first four shocks over an oscillation cycle were constructed through a detailed phase averaged measurement. Such data show a splitting of each shock (except for the first one) into two weaker ones through a ‘moving staircase-like’ motion. During a cycle of motion the downstream shock progressively fades away while a new shock appears upstream. Spark schlieren photographs demonstrate that a periodic convection of large organized vortices over the shock train results in the above described behaviour. An analytical formulation is constructed to determine the self-excitation of the jet column by the screech sound. The screech waves, while propagating over the jet column, add a periodic pressure fluctuation to the ambient level, which in turn perturbs the pressure distribution inside the jet. The oscillation amplitude of the first shock predicted from this linear analysis shows reasonable agreement with the measured data. Additional reasons for shock oscillation, such as a periodic perturbation of the shock formation mechanism owing to the passage of the organized structures, are also discussed.

Nonlinear Strong Shock Interactions: A Shock-Fitted Approach

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M1, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM1 > 1.

An analytic description of converging shock waves

The similarity solution describing the motion of converging spherical and cylindrical shocks is governed by a set of three ordinary differential equations. Previous descriptions of the shock motion have been based on numerical solutions of these differential equations. In the present paper a study of the singular points of the differential equations leads to an analytic description of the flow and a determination of the similarity exponent which is in excellent agreement with the earlier numerical values. Limiting values of the ratio of specific heats are considered. It is shown that as the ratio tends to unity the shock becomes ‘freely propagating’ and the first terms in a power series for the similarity exponent are obtained. Large values of the ratio of specific heats are briefly considered and provide a further check on the analytic description of this paper. Finally in the Appendix the condition for the pressure to have a maximum is clarified and the location of the maximum provides further strong evidence of the high accuracy of the analytic approach of this paper.

人間共存ロボットマニピュレータの衝突安全設計と制御

This paper describes a design methodology for a human-symbiotic robot manipulator which mainly focuses on guarantee of human's safety and abilities of human-robot collaboration. In this paper, we classify the safety design parameters into four categories, such as shock absorption materials, motion controls, collision statements, and safety indices.First, physical models of shock absorption covers, realization of emergency stop and passive impedance control, experimental conditions of generalized human-robot collision, and severity indices for producing moderate injury are described. Next, human-robot collisions are simulated through a combination of there parameters, and the effects of each parameter on anticollision safety are arranged. Then, the several remarks for deciding design parameters are conducted from the experiment and simulation results.As the summarization of this paper, a safety design and control methodology for human symbiotic robot manipulator is proposed by synthesizing these remarks.

Linear stability analysis in transonic diffuser flows

The purpose of this paper is to give the first results of a linear stability analysis which has been applied to the problem of shock oscillations in a transonic diffuser flow. The mean flow is calculated with a numerical code solving the averaged Navier-Stokes equations, but the proposed stability approach is limited to the core region where the viscous effects can be neglected. In order to validate the present approach, the results are compared with Sajben's experimental results and those numerically obtained by Liou and Coakley. It is the first time that these published results are compared with a simple linear stability analysis. As demonstrated below, the shock motion spectra have been correctly reproduced and the frequencies of 200 Hz and 300 Hz have been clearly obtained for the diffuser lengths of l h = 13 and l h = 8.6 respectively. As far as stability of the mean flow is concerned, the temporal amplification rate is always negative, the mean flow is therefore linearly stable. Finally, the amplitude and phase of the fluctuating pressure have been compared. The phase for example is in very good agreement with the experimental results. This can prove that at least in some cases, self-sustained shock oscillations can be explained and predicted with an inviscid linear stability analysis.

VIBRATION REDUCTION AND ISOLATION PERFORMANCE FOR ON–OFF CONTROL OF A FRICTION FORCE AT A SPRING SUPPORT

In order to isolate the vibration transmitted to machines or structures from a floor and to reduce vibration caused by a shock force applied directly to them, a new method of on–off control for the spring support is presented in this paper. The suspension system includes the auxiliary spring and brake mechanism that are designed to control the clamping friction force at the end of the spring. The clamping friction force is varied according to the switching law, which is deduced from the variable structure systems (VSS) control theory. The switching law takes into account the energy dissipation due to friction. In the numerical simulations, the performance of the impulse response reduction and the displacement transmissibility is investigated. The results show that the method is effective in suppressing shock motion and isolating vibration.

Wavelet Analysis of Wall-Pressure Fluctuations in a Supersonic Blunt-Fin Flow

Measurements of wall-pressureuctuations in a Mach 3 ¯ ow over a blunt ® n wereanalyzed with the continuous wavelet transform. This technique offers a fresh approach to the problem of inferringow structure from the wall-pressure signal. The time scales associated with large-scale structures in theow turbulence and with shock crossing events are identi® ed as distinct local maxima in the distribution of energy over the wavelet scales. By using the extrema in the wavelet spectrum as a reference, the signal can be ® ltered in the space of wavelet scales to separate the contribution to the pressureuctuations ofow turbulence and separation shock motion.

Temperature, Size, and Energy of the Shoemaker–Levy 9 G-Impact Fireball

The fortunate position of the Galileo spacecraft provided us with a unique opportunity to directly observe the Shoemaker–Levy 9 impacts as they occurred on the far side of Jupiter, and we present observations of the G fireball obtained by the Near Infrared Mapping Spectrometer (NIMS). These measurements were performed using 10 spectral bands, 4 representing continua and spanning the wavelength range 1.84 to 4.38 μ. Fireball signals were evident for up to 80 sec, with the time of intensity maxima and duration being greater for longer wavelengths. Color temperatures and effective emitting areas were estimated by fitting blackbody functions at the four continuum wavelengths. Good blackbody fits were found, and their intensities at shorter wavelengths show excellent agreement with the Galileo Photopolarimeter/Radiometer measurements. Temperatures near the beginning are above 3000 K, decreasing to ∼1000 K after 1 min. The corresponding areas range from 400 to 20,000 km2. The effective diameter of the luminous fireball shows approximately linear time variation, at least for the first 45 sec. From the temperature–effective diameter relation we find an adiabatic coefficient of γ = 1.2 ± 0.1, much as expected from theoretical considerations. The luminosity, when integrated over the period of observations and assuming a Stephan—Boltzmann radiator, gives an above-cloud radiative energy loss of 0.48 ± 0.13 × 1025erg.As a conceptual aid, we developed a simple, heuristic theory of the fireball phenomenon, considering the penetrating fragment's wake (termed debris channel) to consist of high-temperature jovian and cometary material, which undergoes radial expansion and acceleration back along the wake axis. The outer layer of the material in this debris channel is presumed optically thick, radiating as a blackbody to produce the observed emissions (we speculate that the opacity is produced by condensed refractories such as MgO and SiO2, probably containing impurities). One-dimensional, variable-area axial flow of a radiating, compressible, inviscid gas is concurrently solved with the radial shock motion occurring in the non-axisymmetric atmosphere. We calculate debris surface radii and velocities using Sedov's theory for line explosions. The assumed initial debris surface temperature is consistent with entry shock heating. Our simple model shows good agreement with the observations, for both the temperature and luminous area, and suggests that the diameter of the G fragment (assumed spherical and of unit density) was 300 ± 100 m, with a nominal energy of 2.5 × 1026erg. The measured luminous energy is within a factor of 2 of that predicted for the nominal impactor size, whereas the amount of water in the splashback, as measured by G. L. Bjorakeret al. (1996,Icarus121,411–421) and Th. Encrenazet al., (1997,Planet. Space Sci.) agrees to a factor of 3 with the model results; however, the large CO abundance obtained by E. Lellouchet al. (1995,Nature373,592–595) is inconsistent with the suggested size. This diameter estimate must be considered provisional and probably a lower limit; precise estimates require comparison of the measurements with comprehensive numerical simulations, which we encourage.

High‐latitude ionospheric transient events in a global context

This paper presents a comprehensive global study of bow shock motion, magnetosheath dynamic pressure variations, dayside magnetospheric magnetic field perturbations, and cosmic noise absorption events attending a sequence of transient events observed in high‐latitude global ground magnetograms on February 14, 1986. ISEE 2 spacecraft observations indicated that most of the transient ground magnetometer events were associated with abrupt inward and outward motions of the dawn bow shock during a prolonged period of strongly northward and orthospiral interplanetary magnetic field orientation. Geosynchronous GOES 5 and 6 magnetometer observations provide evidence for corresponding compressions and expansions, which propagated duskward through the prenoon magnetosphere. The magnetopause moved inward past the CCE spacecraft during some of the compressions. The compressions scattered magnetospheric particles and thereby produced quasi‐periodic oscillations in the cosmic noise absorption recorded by high‐latitude ground riometers. We infer that (unobserved) strong transient variations in the solar wind dynamic pressure produced the various phenomena and that the ground magnetometer signatures are best explained in terms of the pressure pulse model of Southwood and Kivelson [1990], in which a single sharp change in the solar wind dynamic pressure generates a pair of field‐aligned currents.

Heliospheric termination shock motion in response to LISM variations: Spherically symmetric model

The unsteady spherically symmetric one‐dimensional gasdynamic model appears to be a powerful tool in the investigation of the termination shock motion. Such a model has previously been used to examine the response of the heliospheric termination shock to variations in upstream solar wind conditions [Ratkiewicz et al., 1996]. In the current paper we apply the same model to study response of the shock to variations in the interstellar medium. The initial‐boundary conditions for the unsteady calculations are given by the pressure as a function of time on an outer boundary either alone or with the density as a function of time on an inner boundary. The motion of the termination shock is caused by fluctuations in both solar wind and interstellar plasma parameters and has a rather complicated behavior, characterized by a sequence of perturbations that hit the termination shock and are reflected from the outer boundary.

New methods for diagnosing and controlling hohlraum drive asymmetry on Nova

A novel method to control lowest-order (P2) flux asymmetry in Nova cylindrical hohlraums [E. M. Campbell et al., Rev. Sci. Instrum. 57, 2101 (1986)] with fixed laser beams is to use a pair of axial gold disks of varying radii to partially block the capsule view of the laser-entrance holes. Some advantages in using axial disks include the prospect for added drive on target, the potential for P4 control when used in tandem with laser pointing, and possibly reduced time-dependent P2(t) flux asymmetry swings at early time. Neutron-based diagnostics have provided some suggestion of increased drive, but a more direct measure of drive enhancement is with the use of backlit, low-density (0.3 g/cc) foam surrogate targets. In this scheme, an ablatively driven, inwardly propagating shock is imaged in time using backlighting from an irradiated Ti disk placed outside of the hohlraum. The benefit in using low-density surrogate targets is an amplified shock speed that enables easier detection of both average shock motion (drive) and distortion (flux asymmetry). Experiments and calculations are in excellent agreement over a nearly 10% enhancement in peak drive temperature in the presence of axial gold disks. Measurements of lower-order distortion, P2(t) and P4(t), versus time for several laser pointings (without axial disks) using this technique have also been carried out and show good agreement between experiment and simulations. Efforts to further control time-dependent flux asymmetry using multiple ring, beam-phasing techniques on Nova, as will be required for the National Ignition Facility [J. Lindl, Phys. Plasmas 2, 3933 (1995)], are under development. Current designs indicate an appreciable reduction in P2(t) is possible. Significant control of time-integrated P4 flux asymmetry with appreciable inner and outer ring separation also appears possible.

Unsteady Flow and Shock Motion in a Transonic Compressor Rotor

The results of an experimental and numerical comparison of the unsteadiness and shock motion that occurs in the tip region within a modern, low-aspect-ratio, high-through-e ow, axial-e ow transonic fan rotor are presented. The unsteadiness studied here is associated with local phenomena within the blade passage and not related to blade row interaction. Unsteady static pressures were measured at the casing over the rotor that operates at a tip relative Mach number of 1.6. An unsteady three-dimensional Navier ‐ Stokes computational study was performed with tip clearance comparable to the test rotor. The fully three-dimensional, unsteady, Reynolds-averaged Navier ‐ Stokes equations were solved with time steps, each nominally of 2.8 3 10 25 s in duration or approximately e ve times blade pass frequency. The results in the clearance gap were retained from the computational solution and compared with the experimental measurements. Both indicated deterministic unsteadiness near the location of the shock. High levels of unsteadiness were also measured downstream of the shock in the path of the clearance vortex, but this phenomenon was not predicted by the computation. The unsteadiness near the shock was shown to be a result of movement of the shock. The amplitude and frequency of shock position oscillation was estimated from the results to be about 2% chord and 2 kHz, respectively. Analysis of loss caused by the shock unsteadiness suggested that losses because of shock motion were insignie cant relative to the steady shock loss at the relative Mach number studied.

A212 超音速ノズルにおける衝撃波の振動の微細機構の可視化

To investigate shock oscillation mechanism in supersonic nozzle, high speed CCD camera is used with schlieren system. Power spectral density distributions of shock displacement and cross-correlation between shock displacement and light intensities at various points are obtained. As a result, it is clarified that shock oscillation mechanism consists of downstream moving large scale turbulent structure generated due to shock motion and disturbance propagating upstream in core flow region.

Studies of the Martian bow shock response to the variation of the magnetosphere dimensions according to TAUS and MAGMA measurements aboard the Phobos 2 orbiter

A self-consistent quantitative model is presented which describes the planetary bow shock motion and its shape variation due to variations of the external plasma flow parameters and the magnetopause shape. This model is applied to the analysis of the Martian bow shock motions and for the explanation of its unusual properties.

Analytical Model of Unsteady Shock Motion on Hypersonic Forebodies

The behavior of an unsteady shock associated with the surface of the forebody of a hypersonic vehicle is modeled analytically. The present study develops a simple engineering model, based on the nonlinear oscillator theory, to perform a dynamic analysis on nonuniform e ow over two-dimensional hypersonic forebodies. The emphasis is on exploring the e uid physics while avoiding time-intensive computational techniques for unsteady calculations. Closed-form solutions of the shock motion are derived and any coupling phenomena between the boundary layer and the shock are studied by including viscous effects in the analysis. The response of the shock to different freestream Mach numbers, frequencies, and amplitudes of perturbation is examined. A quasisteady approach and piston analogy have been incorporated. It is shown that the amplie cation factor of the inviscid shock relative to the surface matches with the computational results within 10% accuracy under similar conditions.