Shock Motion Research Articles

PLASMA IN THE HELIOSHEATH: 3.5 YEARS OF OBSERVATIONS

Voyager 2 (V2) has observed heliosheath (HSH) plasma since 2007 August. We describe how the plasma has evolved across the HSH. We show that the low solar wind dynamic pressure leads to an inward movement of the termination shock (TS) of about 10 AU to a minimum position of 73 AU in 2010. Near the TS large fluctuations are present in the HSH, but these fluctuations decrease as V2 moves further from the TS. The radial speed slowly decreases and the plasma flow slowly turns tailward. The temperature decreases across the HSH. The radial speed in 2011 remains above 100 km s(-1), which implies that V2 is a substantial distance from the heliopause.

An experimental study of buzz instability in an axisymmetric supersonic inlet

An experimental study was carried out on an axisymmetric supersonic inlet with external compression. The scope of this study was to investigate the general characteristics of the inlet buzz under various design and off-design conditions. The model was equipped with accurate and high frequency pressure sensors and the tests were conducted at Mach numbers varying from 1.8 to 2.5, at various angles of attack, and at different mass flow rates. Shadowgraph flow visualization, together with a high speed camera, was used to capture the external shock structure in front of the inlet. Frequencies of buzz were obtained from both the shadowgraph pictures and analysis of the pressure data. The amplitude of the shock wave motion was measured from the visualization pictures, too. The results show that for low mass flow rates, buzz frequency is almost independent of Mach number, while at a higher mass flow rate, the frequency of the shock oscillation increases with Mach number. Further, for each free stream Mach number, as the mass flow rate decreased, the amplitude of the shock movement grew, but its frequency decreased.

Time-resolved stereo PIV measurements of shock–boundary layer interaction on a supercritical airfoil

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave–boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 × 106 are analyzed regarding the origin and nature of the unsteady shock–boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa.

Low-order stochastic modelling of low-frequency motions in reflected shock-wave/boundary-layer interactions

A combined numerical and analytical approach is used to study the low-frequency shock motions observed in shock/turbulent-boundary-layer interactions in the particular case of a shock-reflection configuration. Starting from an exact form of the momentum integral equation and guided by data from large-eddy simulations, a stochastic ordinary differential equation for the reflected-shock-foot low-frequency motions is derived. During the derivation a similarity hypothesis is verified for the streamwise evolution of boundary-layer thickness measures in the interaction zone. In its simplest form, the derived governing equation is mathematically equivalent to that postulated without proof by Plotkin (AIAA J., vol. 13, 1975, p. 1036). In the present contribution, all the terms in the equation are modelled, leading to a closed form of the system, which is then applied to a wide range of input parameters. The resulting map of the most energetic low-frequency motions is presented. It is found that while the mean boundary-layer properties are important in controlling the interaction size, they do not contribute significantly to the dynamics. Moreover, the frequency of the most energetic fluctuations is shown to be a robust feature, in agreement with earlier experimental observations. The model is proved capable of reproducing available low-frequency experimental and numerical wall-pressure spectra. The coupling between the shock and the boundary layer is found to be mathematically equivalent to a first-order low-pass filter. It is argued that the observed low-frequency unsteadiness in such interactions is not necessarily a property of the forcing, either from upstream or downstream of the shock, but an intrinsic property of the coupled system, whose response to white-noise forcing is in excellent agreement with actual spectra.

Numerical study of shock-turbulent boundary layer interactions with incipient and complete separation

This paper aims at describing the main features of a separated boundary layer in shock reflection at a Mach number of 2.3. The data used for this analysis were taken from large eddy simulations of the interactions for three-shock intensities, resulting in flow cases from incipient to fully separated. Computational results were validated versus experimental data. The main space-time properties of the reflected shock motion are described together with their link with the other flow regions. The analysis of the correlations between the shock motion and the unsteady pressure field provides information about the origins of shock unsteadiness.

Application of fast-responding pressure-sensitive paint to a hemispherical dome in unsteady transonic flow

The current work focuses on the development and application of fast-responding polymer/ceramic pressure-sensitive paint (PSP) as an advanced surface pressure measurement technique for unsteady flow fields in large-scale wind tunnels. To demonstrate the unsteady PSP technique, the unsteady surface pressure distribution over a hemispherical dome placed in the United States Air Force Research Laboratory’s Trisonic Gasdynamics Facility (TGF) was studied by phase-locking to the characteristic frequency in the flow caused by an unsteady separated shear layer shed from the dome. The wind tunnel was operated at stagnation pressures of 23.92 and 71.84 kPa, with the test section flow at Mach 0.6. Under the two operating conditions, the predominant shear layer frequency was measured to be 272 and 400 Hz, respectively. The quasi-periodic shear layer frequency enabled a phase-averaged method to be employed for capturing the unsteady shock motion on the hemisphere. Unsteady pressure data resulting from this technique are shown to correlate well with measurements acquired by conventional measurement techniques. Measurement uncertainty in the phase-averaging technique will be discussed. To address measurement uncertainties from temperature sensitivity and model movement, a new implementation of an AC-coupled data representation is offered.

과팽창 노즐 내에 발생하는 FSS-RSS 현상에 관한 실험적 및 수치해석적 연구

The interaction patterns between shock wave and boundary layer in a rocket nozzle are mainly classified into two categories, FSS(Free Shock Separation) and RSS(Restricted Shock Separation), both of which are associated with the thrust characteristics as well as side loads of the engine. According to the previous investigations, strong side loads of the engine are produced during the period of transition from FSS to RSS or vice versa. The present work aims at investigating the unsteady behavior of the separation shock waves in a two-dimensional supersonic nozzle, using experimental method and CFD. Schlieren optical method was employed to visualize the time-mean and time-dependent shock motions in the nozzle. The unsteady, compressible N-S equations with SST K-<TEX>$\omega$</TEX> turbulence closure were solved using a fully implicit finite volume scheme. The results obtained show the separation shock motions during the transition of the interaction pattern.

The Emerging Markets’ Investor Sentiment Composite Index: A Test on Bursa Malaysia

During the recent global stock market crash in 2007 to 2008, the MSCI World Index of developed markets fell approximately 50 percent in value; hence the contagion effect to the emerging markets was inevitable that it fell further. In early 2009, the MSCI Emerging Markets Index has fallen 66 percent from peak to trough, which had plunged deeper than the stock markets of developed countries. It would be of no surprises for academics and practitioners to link the local stock markets behaviours to other regional stock markets as one of the contributions in their research papers and write ups. Theoretical wise, it has for decades, a vast number of explanations been offered in attempts to explain the behaviour of asset prices from the perspective of investor’s psychology. The theory of noise trader by Black (1986) and Trueman (1988) initiated the attempt by modeling that noise trading no longer exists as a temporarily shock or short term movement in asset prices as previously discussed in Efficient Market Hypothesis. This paper introduces the investor sentiment composite index constructed specifically for the emerging markets, in particular the Bursa Malaysia. The composite index is constructed comprising of liquidity proxy, the information IPOs and advancer decliners ratio. Unlike the study done on developed market, this paper introduces a measurement of liquidity that has been used in study of liquidity on emerging market by Amivest (1997). A proxy known as oversubscription ratio is taken from the IPO literature is also added that signifies investors demand in the market. Bursa Malaysia is expected to closely represent the emerging markets as to study the impact investor sentiment has on the returns and also the contribution to the bull and bear stock market defined by the leading indicator KLCI.

Ammonia observations of bright-rimmed clouds: establishing a sample of triggered protostars

We observed 42 molecular condensations within previously identified bright-rimmed clouds in the ammonia rotational inversion lines NH3 (1,1), (2,2), (3,3) and (4,4) using the Green Bank Telescope in Green Bank, West Virginia. Using the relative peaks of the ammonia lines and their hyperfine satellites we have determined important parameters of these clouds, including rotational temperatures and column densities. These observations confirm the presence of dense gas towards IRAS point sources detected at submillimetre wavelengths. Derived physical properties allow us to refine the sample of bright-rimmed clouds into those likely to be sites of star formation, triggered via the process of radiatively-driven implosion. An investigation of the physical properties of our sources show that triggered sources are host to greater turbulent velocity dispersions, likely indicative of shock motions within the cloud material. These may be attributed to the passage of triggered shocks or simply the association of outflow activity with the sources. In all, we have refined the Sugitani et al. (1991) catalogue to 15 clouds which are clearly star-forming and influenced by external photoionisation-induced shocks. These sources may be said, with high confidence, to represent the best examples of triggering within bright-rimmed clouds.

A synthetic 21-cm Galactic Plane Survey of a smoothed particle hydrodynamics galaxy simulation

We have created synthetic neutral hydrogen (HI) Galactic Plane Survey data cubes covering 90 degrees < l < 180 degrees, using a model spiral galaxy from SPH simulations and the radiative transfer code TORUS. The density, temperature and other physical parameters are fed from the SPH simulation into TORUS, where the HI emissivity and opacity are calculated before the 21-cm line emission profile is determined. Our main focus is the observation of Outer Galaxy `Perseus Arm' HI, with a view to tracing atomic gas as it encounters shock motions as it enters a spiral arm interface, an early step in the formation of molecular clouds. The observation of HI self-absorption features at these shock sites (in both real observations and our synthetic data) allows us to investigate further the connection between cold atomic gas and the onset of molecular cloud formation.

Focus on sensors and detectors

Focus on sensors and detectors

On high-order shock-fitting and front-tracking schemes for numerical simulation of shock–disturbance interactions

High-order methods that can resolve interactions of flow-disturbances with shock waves are critical for reliable numerical simulation of shock wave and turbulence interaction. Such problems are not well understood due to the limitations of numerical methods. Most of the popular shock-capturing methods are only first-order accurate at the shock and may incur spurious numerical oscillations near the shock. Shock-fitting algorithms have been proposed as an alternative which can achieve uniform high-order accuracy and can avoid possible spurious oscillations incurred in shock-capturing methods by treating shocks as sharp interfaces. We explore two ways for shock-fitting: conventional moving grid set-up and a new fixed grid set-up with front tracking. In the conventional shock-fitting method, a moving grid is fitted to the shock whereas in the newly developed fixed grid set-up the shock front is tracked using Lagrangian points and is free to move across the underlying fixed grid. Different implementations of shock-fitting methods have been published in the literature. However, uniform high-order accuracy of various shock-fitting methods has not been systematically established. In this paper, we carry out a rigorous grid-convergence analysis on different variations of shock-fitting methods with both moving and fixed grids. These shock-fitting methods consist of different combinations of numerical methods for computing flow away from the shock and those for computing the shock movement. Specifically, we consider fifth-order upwind finite-difference scheme and shock-capturing WENO schemes with conventional shock-fitting and show that a fifth-order convergence is indeed achieved for a canonical one-dimensional shock-entropy wave interaction problem. We also show that the method of finding shock velocity from one characteristic relation and Rankine–Hugoniot jump condition performs better than the other methods of computing shock velocities. A high-order front-tracking implementation of shock-fitting is also presented in this paper and nominal rate of convergence is shown. The front-tracking results are validated by comparing to results from the conventional shock-fitting method and a linear-interaction analysis for a two-dimensional shock disturbance interaction problem.

Scaling of response spectrum and duration for aftershocks

Aftershocks have the potential to cause collapse of a structure that has been already damaged by the preceding main shock. Seismic safety of a structure should therefore be ascertained through a damage analysis using the anticipated main shock and few larger-aftershock motions. Simulation of aftershock motions needs characterization of the seismic hazard due to aftershocks, and therefore it will be useful to develop a conditional scaling model that can predict the response spectrum of an anticipated aftershock motion consistent with the design spectrum of the main shock motion anticipated at the same station. In this study an attempt is made to develop a conditional scaling model for the pseudo spectral velocity spectrum via linear regression analysis on the aftershock and main shock recordings for the 1999 Chi–Chi earthquake. It is shown that it may be possible to obtain a simpler and approximate version of the conditional model from an unconditional model. Damage-causing potential of a ground motion also depends on its strong motion duration (SMD) and therefore a conditional scaling model is developed for SMD of the aftershock motion in several narrow frequency-bands. The model is developed for the larger-aftershock motions and it is shown that a reasonable replacement of such a model may be obtainable directly from an unconditional model. Finally, a simple weighted averaging scheme is proposed to obtain the composite SMD from the SMDs for different frequency bands by using the pseudo spectral acceleration spectrum of the motion.

Investigation of large scale shock movement in transonic flow

Large eddy simulations were made of transonic flow over a two-dimensional bump where shock wave/turbulent boundary layer interaction takes place. Different flow conditions were investigated to find conditions for large scale shock movement. The innermost part of the shock was found to be moving for sufficiently strong shocks. None of the cases display large scale movement of the whole shock.

Harmonic Balance Analysis of Blade Row Interactions in a Transonic Compressor

In this paper we apply the harmonic balance technique to analyze an inlet guide vane and rotor interaction problem, and compare the computed flow solutions to existing experimental data. The computed results, which compare well with the experimental data, demonstrate that the technique can accurately and efficiently model strongly nonlinear periodic flows, including shock/vane interaction and unsteady shock motion. Using the harmonic balance approach, each blade row is modeled using a computational grid spanning just a single blade passage regardless of the actual blade counts. For each blade row, several subtime level solutions that span a single time period are stored. These subtime level solutions are related to each other through the time derivative term in the Euler (or Navier―Stokes) equations, which is approximated by a pseudo-spectral operator, by complex periodicity conditions along the periodic boundary of each blade row's computational domain, and by the interface boundary conditions between the vane and rotor. Casting the governing equations in harmonic balance form removes the explicit dependence on time. Mathematically, the equations to be solved are similar in form to the steady Euler (or Navier―Stokes) equations with an additional source term proportional to the fundamental frequency of the unsteadiness. Thus, conventional steady-state computational fluid dynamics techniques, including local time stepping and multigrid acceleration, are used to accelerate convergence, resulting in a very efficient unsteady flow solver.

Instability of shock-induced nozzle flow separation

We investigate experimentally the causes of jet plume instability and enhanced mixing observed in the exhaust of shock-containing convergent-divergent nozzles. Key features of the internal flow are the separation shock, separation shear layers, and pattern of alternating expansion and compression waves downstream of the shock. We focus on two possible reasons for this instability—the motion of the separation shock and the wave pattern downstream of the shock. The nozzle flow was generated in a planar facility with variable area ratio and pressure ratio, and the motion of the shock was tracked using time-resolved wall pressure measurements. The isolated effect of the wave pattern was investigated in a separate facility wherein a sonic shear layer, simulating the nozzle separation shear layer, was disturbed with compression and expansion waves emanating from a wavy wall. In both instances, the instability of the shear layer was characterized by time-resolved measurements of the total pressure. In the nozzle flow, the amplitude of shock motion increases with shock strength. Correlation of shock motion with shear layer total pressure is virtually absent for weak shocks but becomes significant for strong shocks. However, impingement of stationary waves on the shear layer had no impact on its growth rate. We conclude that the enhanced shear layer instability is strongly coupled to shock motion, and that the wave pattern by itself is not a cause of enhanced mixing. The occurrence of asymmetric separation at large shock strengths is a further contributor to the enhancement of instability.

A gPC-based approach to uncertain transonic aerodynamics

The present paper focus on the stochastic response of a two-dimensional transonic airfoil to parametric uncertainties. Both the freestream Mach number and the angle of attack are considered as random parameters and the generalized Polynomial Chaos (gPC) theory is coupled with standard deterministic numerical simulations through a spectral collocation projection methodology. The results allow for a better understanding of the flow sensitivity to such uncertainties and underline the coupling process between the stochastic parameters. Two kinds of non-linearities are critical with respect to the skin-friction uncertainties: on one hand, the leeward shock movement characteristic of the supercritical profile and on the other hand, the boundary-layer separation on the aft part of the airfoil downstream the shock. The sensitivity analysis, thanks to the Sobol’ decomposition, shows that a strong non-linear coupling exists between the uncertain parameters. Comparisons with the one-dimensional cases demonstrate that the multi-dimensional parametric study is required to get the correct shape and magnitude of the standard deviation distributions of the flow quantities such as pressure and skin-friction.

An experimental study of transonic shock/boundary layer interactions subject to downstream pressure perturbations

An experimental study of the response to downstream pressure perturbations of transonic shocks in a parallel walled duct has been conducted. Tests have been carried out for normal shock strengths of M ∞ = 1.4 and 1.5 with pressure perturbation frequencies in the range 16–90 Hz. The measurement techniques of high speed schlieren photography, laser Doppler anemometry and high frequency pressure measurements have been used. In all test cases, the normal shock undergoes periodic oscillatory motion in the streamwise direction. The interaction structure between the oscillating shock and the tunnel wall turbulent boundary layer varies during oscillations, especially at M ∞ = 1.4 , where the leading shock–leg of the lambda shock–foot structure gets significantly stronger during upstream shock motion and weaker during downstream motion. These changes are related to the relative strength of the shock (which varies due to the velocity of shock motion) and the effect that this has on the extent of boundary layer thickening and/or shock induced boundary layer separation. The dominant mechanism that governs the dynamics of shock motion in response to downstream pressure perturbations has also been identified and explains why the amplitude of shock motion decreases with increasing frequency.

폭발파에 의한 음향파 생성 메커니즘의 수치적 연구

The goal of this paper is to investigate the generation characteristics of the main impulsive noise sources generated by the supersonic flow discharging from a muzzle. For this, this paper investigates two fundamental mechanisms to sound generation in shocked flows: shock motion and shock deformation. Shock motion is modeled numerically by examining the interaction of a sound wave with a shock. The numerical approach is validated by comparison with results obtained by linear theory for a small disturbance case. Shock deformations are modeled numerically by examining the interaction of a vortex ring with a blast wave. A numerical approach of a dispersion-relation-preserving(DRP) scheme is used to investigate the sound generation and propagation by their interactions in near-field.

Dependence between the shock and the separation bubble in a shock wave boundary layer interaction

We present experimental results obtained in a turbulent boundary layer at a Mach number of 2.3 impinged by an oblique shock wave. Strong unsteadiness is developed in the interaction, involving several frequency ranges which can extend over two orders of magnitude. In this paper, attention is focused on the links between the low-frequency shock motions and the separation bubble, in particular phase relationships are evaluated. An interpretation based on a simple scheme of the streamwise evolution of the instantaneous pressure is proposed. As it is mainly based on the pressure signal properties inside the region of the shock oscillation, it may be expected that it will still be relevant for different configurations of shock-induced separation as compression ramp, blunt bodies, or over expanded nozzles.