Shock Motion Research Articles

Transonic Shock Wave Patterns Over an Airfoil in an Accelerated Flow

It is well known that in a high subsonic flow over an airfoil, there exists a local supersonic pocket and similarly in a supersonic flow over the same, there exists a local subsonic pocket. But, how the transonic shock wave pattern over the airfoil changes when the freestream flow accelerates uniformly from high subsonic to supersonic - i.e. how a subsonic flow with a supersonic pocket changes into a supersonic flow with a subsonic pocket- is not reported so far. This study is an attempt to explore the above phenomena. In order to study the accelerated flow, Navier-Stokes equations are extended to acceleration frame of reference. Using these equations, numerical simulation of transonic flow over NACA0012 airfoil is carried out with freestream acceleration. The influence of acceleration on the flow field is studied with different levels of acceleration and retardation. This study revealed that both acceleration and retardation do influence the movement of transonic shock movement, and it is more pronounced in high levels of retardation. But, the shock wave pattern during the change from high subsonic to supersonic remains the same for various levels of acceleration. The continuous change of shock wave pattern over the airfoil is visualized in a single simulation and the underlying physical phenomena are investigated.

Non-stationary shock motion unsteadiness in an axisymmetric geometry with pressure gradient

Shock wave/boundary layer interaction (SWBLI) is studied in a large area-ratio axisymmetric nozzle comprising a design exit Mach number of 5.58. Shock motion unsteadiness is captured by way of the dynamic wall pressure and is evaluated during overexpanded operations up to a nozzle pressure ratio of 65. Stationary SWBLI is first considered at a nozzle pressure ratio of 28.7 such that the internal flow structure is in a restricted shock separated state; the mean position of the annular separation shock resides at a fixed position. Conditional averages of the wall pressure fluctuations show how the motion of the incipient separation shock is out of phase with pressure fluctuations measured in the separated region downstream of the shock; pressure decreases when the shock moves downstream and vice versa. This is indicative of a long intermittent region, in terms of the boundary layer thickness, as the observed phenomena can be explained by translating the static wall pressure profile along with the shock motion. Non-stationary SWBLI is then considered by increasing the nozzle pressure ratio over time (transient start-up). Under these conditions, the shock pattern varies in strength and structure as it sweeps through the nozzle. A time-frequency analyses of the fluctuating wall pressure during the non-stationary operations, and at the same location that the stationary unsteadiness is analyzed, reveals a similar spectral footprint. However, for relatively slower start-ups, the amplitude of the unsteadiness is reduced by a factor of about seven. The findings demonstrate how the rate at which the nozzle pressure ratio increases can have a significant influence on the amplitude of the unsteady shock foot motion.

A transport approach for analysis of shock waves in cellular materials

This paper is concerned with a new approach for analytical modelling of shock-like behaviour encountered with high velocity crushing of cellular materials. The presented methodology is founded on integral transport equations which describe the response of a control volume moving inside another moving control volume and thus provides a technique for the direct handling of material discontinuities such as shock waves. The transport approach (being based on integration as opposed to differentiation) is shown to readily accommodate discontinuities in physical fields. Control volume movement is described by means of judiciously defined velocity fields that account for shock movement and domain distortion. A feature of the approach is the realisation of governing differential equations whose derivatives reflect the movement of the transporting control volume, which also serve as a means to establish the exactness of proposed solutions.The transport approach is applied to investigate issues raised in the literature concerning discrepancies in results obtained from momentum and energy approaches. The ability of the transport approach to enforce global balances of energy and momentum reveal the correct approach to shock modelling in cellular materials. The efficacy of the method is demonstrated through its application to three case studies. The first two cases involve impact applied to the well-known Taylor-cellular bar and a rigid mass on a cellular bar; the results of which are shown to be exact agreement with the solutions provided in the literature. The third case study presents a new analytical solution for impact involving compacted material described with a Bingham plasticity model.

Prediction of Nonequilibrium Air Plasma Radiation Behind a Shock Wave

The absolute radiation measurements obtained in the electric arc-driven shock-tube facility at NASA Ames Research Center were analyzed to test the collisional-radiative model developed at École Centrale Paris. Two conditions representative of Earth reentry at 10.54 and were investigated in the vacuum ultraviolet and infrared spectral ranges. For each of the conditions, the corresponding charge-coupled device images were analyzed. The electron number density was inferred from Stark-broadened nitrogen and lines. Comparisons with the predicted electron number density profiles enabled us to validate the ionization rate constant model implemented in the flowfield solver and to accurately locate the shock front. For both freestream conditions and all the spectral ranges, the predictions of the initial intensity rises were improved when the total spatial smearing (due to the shock motion, the optics, and the camera) was taken into account. The nonequilibrium intensities observed in the vacuum ultraviolet and infrared spectral ranges were underpredicted by the collisional-radiative model when only electron-impact excitation and ionization processes were taken into account. Then, the effect of heavy-particle impact processes was studied by applying various multitemperature dissociation rate constant and vibration–dissociation coupling models as well as heavy-particle impact excitation models. The nonequilibrium peak intensities observed in the vacuum ultraviolet and infrared spectral ranges were shown to be controlled by heavy-particle impact excitation processes.

The Earth's bow shock velocity distribution function

AbstractIt is well established that interplanetary disturbances cause the Earth's bow shock to move sunward or earthward. Since the launch of the Cluster mission, precise determination of the shock velocity was carried out allowing for the possibility to perform sophisticated investigations about the shock dynamics. The shock normal and velocity are determined for 381 Earth's bow shock crossings using data from the Spatio Temporal Analysis of Field Fluctuations ‐ Spectrum Analyzer experiment on board the Cluster spacecraft. We have found that the observed radial shock velocity is well fitted by a Maxwellian for speeds less than 80 km s−1. The Maxwellian fit provides a standard deviation km s−1. Assuming that the shock motion is exclusively controlled by the time rate of change of solar wind ram pressure, a probability density for the shock velocity near the nose region is constructed using the basic elements of probability theory. The obtained results are in a very good agreement with the observations when typical conditions of the solar wind are considered. The present study indicates that the ram pressure is a predominant parameter in shock dynamics and the relevance of the Mach number is not a determinant.

The use of dynamic basis functions in proper orthogonal decomposition

Currently, the usefulness of proper orthogonal decomposition (POD) is limited to computational domains with fixed meshes and fixed boundaries. This paper presents a new POD method that enables the modeling of flow through computational domains with deforming meshes and/or moving boundaries. To achieve this goal, the solution is approximated using basis functions which, although not explicitly functions of time, depend on parameters associated with flow unsteadiness. Results are shown for transonic flow through the Tenth Standard Configuration. Comparisons are made between this method and the standard approach for on- and off-reference flow conditions. This method properly captured flow nonlinearities and shock motion for cases in which the classical POD method failed.

Noise of an Overexpanded Mach 3.3 Jet: Non-Linear Propagation Effects and Correlations with Flow

The noise emitted by an overexpanded round jet at a Mach number of 3.3 and a Reynolds number of 105, computed in a previous study using large-eddy simulation (LES), is investigated. In a first step, the non-linear sound propagation effects are quantified by performing two far-field wave extrapolations from the LES near-field data. The extrapolations are carried out by solving the linearized Euler equations in one case and the full Euler equations in the other, without atmospheric absorption, up to a distance of 240 radii from the jet nozzle exit. The non-linear effects are shown to be quite significant, resulting in a series of N-shaped waves in the pressure signals, and in weaker mid-frequency components and stronger high-frequency components in the spectra. Close to the peak directivity radiation angle, for instance, they lead to about a 8 dB loss and a 6 dB gain at the Strouhal numbers of 0.2 and 1, respectively. In a second step, noise generation mechanisms are discussed by calculating correlations between far-field pressure fluctuations and turbulent quantities in the jet. High levels of correlation are found with the centerline flow fluctuations at the end of the potential core, with the shear-layer flow fluctuations over a large axial distance, and with the centerline density fluctuations between the 3rd and the 5th shock cells. They are attributed to the intermittent intrusion of low-speed vortical structures in the potential core, to the supersonic convection of turbulent structures, and to the shock motions at the screech tone frequency.

Development and application of a point Doppler velocimeter featuring two-beam multiplexing for time-resolved measurements of high-speed flow

A novel point Doppler velocimeter (pDV) based upon the Doppler global velocimetry principle is presented, which is capable of three-component velocity vector measurements at 100 kHz mean rates over extended time periods. In this implementation, two laser beams are multiplexed to illuminate the flow over alternating time windows, providing for a reduction in the number of sensors required. The implications of this multiplexing paradigm coupled with the fundamental limits set by the optical absorption filter are examined in detail, and uncertainties are predicted via instrumentation modeling and representative synthetic flow data. The results indicate that the multiplexing pDV instrument provides the required temporal and velocity resolution for turbulent shear flows at velocities of nominally 500 m/s. As a demonstration and validation of this time-resolved technique, statistics of three-velocity component measurements in a cold, supersonic, over-expanded jet at jet exit Mach number M j = 1.4 (design Mach number M d = 1.65) are presented. Time resolution up to 250 kHz and instantaneous velocity uncertainties between 6.6 and 11.1 m/s were obtained. Comparisons of mean pDV data with laser Doppler velocimetry data are consistent with uncertainty predictions for the technique. The ultimate value of the instrument is exhibited in the analysis of Reynolds stress spectra in the screeching jet, exposing the spatial development of motions at the harmonics of the screech tone, variable phase-coordinated shock motions, and growth of turbulent fluctuations in the developing shear layer of the jet. From the data presented, the screech tone phenomenon is suspected to be linked to the production of radial–azimuthal shear stresses in extended regions beyond the potential core.

Unsteady shock motions in an over-expanded parabolic rocket nozzle

An experimental investigation has been conducted to identify a new flow condition in free shock separation that is found to contribute significantly towards the overall flow unsteadiness in a thrust optimized parabolic nozzle at certain operating conditions. Cold gas tests were conducted with a 1/10th scale, area-ratio 30 thrust optimized parabolic nozzle both under sea-level and high-altitude conditions. Although the latter tests showed absence of fully formed restricted shock separation at any operating condition unlike sea-level tests, the peak rms values at certain operating conditions were still seen to be considerably high and comparable with those experienced during flow transitions in sea-level tests. A detailed statistical analysis of the data revealed that the separated shear-layer in free shock separation condition can come in very close proximity to the nozzle wall but at no point of time randomly impinges on it. This sets the entire back-flow region into pressure fluctuations that is seen to increase the length of intermittent region as well as the overall flow unsteadiness considerably. This in turn is strictly dictated by the relative locations of the normal shock to the separation shock which induce the necessary momentum imbalance of flow across each of these shocks to move the separated shear layer within critical proximities of the nozzle wall. Beyond this critical limit, flow reattachment occurs and a transition from free shock separation to fully formed restricted shock separation occurs.

Experimental investigation of the transonic flow around the leading edge of an eroded fan airfoil

The influence of leading edge modification on the time-averaged and instantaneous flow around a fan airfoil is investigated by particle image velocimetry (PIV), schlieren imaging and high-speed shock shadowgraphs in a transonic cascade windtunnel. In addition to a global characterization of the time-averaged flow using PIV, the instantaneous passage shock position was extracted from single-shot PIV measurements by matching the tracer velocity across the normal shock with an exponential fit. The instantaneous shock positions are assigned to a probability density distribution in order to obtain the average position and the range of fluctuations of the eroded and reference leading edge. The profiles are used to estimate the response time of the particles to the normal shock which was found to be in the sub-microsecond range. Averaged PIV measurements and the probability density of shock position from both geometries are obtained at near stall and choked conditions. In order to extract the frequency range of the shock motion, the shadow of the shock wave was tracked using high-speed shadowgraphy. The paper also provides details on the experimental implementation such as a specifically designed light-sheet probe.

A proper orthogonal decomposition method for nonlinear flows with deforming meshes

This paper presents a proper orthogonal decomposition (POD) method that uses dynamic basis functions. The dynamic functions are of a prescribed form and do not explicitly depend on time but rather on parameters associated with flow unsteadiness. This POD method has been developed for modeling nonlinear flows with deforming meshes but can also be applied to fixed meshes. The method is illustrated for subsonic and transonic flows in channels with fixed and deforming meshes. This method properly captured flow nonlinearities and shock motion for cases in which the classical POD method failed.

Experimental Identification of Transient Dynamics for Supersonic Inlet Unstart

Successful realization of dual-mode scramjet engines will require closed-loop control schemes to eliminate the occurrence of inlet unstart. An important step toward this goal is the development of dynamic models for shock system motion inside the inlet isolator under varying flow conditions. In this paper, shock motion models are developed based on fast-response pressure measurements made along the wall of the isolator (straight channel) downstream of a Mach 1.8 nozzle. The shock system can be perturbed by changing the stagnation pressure with an upstream valve and/or by changing the backpressure with a downstream flap. In particular, the shock’s transient dynamics are modeled, which govern the unstart process and are induced by changing pressure-boundary conditions, by employing system identification techniques. The result is a partially nonlinear dynamic model that reveals the possibility of partitioning the nonlinear behavior from the linear dynamics with relative ease. A second dynamic model is then generated, where the nonlinear portion has been prespecified, leaving only the linear portion to be determined by system identification. The modeling and identification process specific to the experimental unstart data used are discussed and successful models are presented for both the full system identification and the partitioned model cases.

Prescribed Velocity Method for Simulation of Aerofoil Gust Responses

A new method for modeling the interaction of an aerofoil with a gust using a prescribed velocity approach, called the split velocity method is presented. This approach effectively rearranges the governing equations into a form that allows for more efficient calculation and includes both the effect of the gust on the aerofoil and the effect of the aerofoil on the gust. The convection of gusts, through the domain from the far field, is investigated using the new method for a range of 1-cosine gusts. The results obtained are compared to an existing prescribed velocity approach called the field velocity method, which neglects the effect of the aerofoil on the gust. The two prescribed velocity approaches agree well for longer gusts. For shorter gusts where the gust length is close to the chord of the aerofoil, the new approach produces better results. Details of a linearized version of the split velocity method are also given. The linearized version is shown to agree well with the full method for cases when the gust does not result in large shock motions.

Spectral Characteristics of Separation Shock Unsteadiness

Spectra of wall-pressure fluctuations caused by separation shock unsteadiness were compared for data obtained from wind-tunnel experiments, the Hypersonic International Flight Research Experimentation flight test 1, and large-eddy simulations. The results were found to be in generally good agreement, despite differences in Mach number and two orders of magnitude difference in Reynolds number. Relatively good agreement was obtained between these spectra and the predictions of a theory developed by Plotkin. The predictions of this theory are also qualitatively consistent with the results of experiments in which the shock motion was synchronized to controlled perturbations. The results presented here support the idea that separation unsteadiness has common features across a broad range of compressible flows and that it behaves as a selective amplifier of large-scale disturbances in the incoming flow.

Bistability and Hysteresis in a Nonlinear Dynamic Model of Shock Motion

The study is motivated by a review of experimental and numerical evidences for the occurrence of bistability and hysteresis in supersonic inlets. By retaining the essential strongly nonlinear behaviors and the dominant system dynamics, a low-order model of the time-dependent behaviors of shock motion is developed to describe the bistability and hysteresis behaviors of shock motion in a supersonic inlet. Assumptions of inviscid and quasi-one-dimensional flow are invoked to ensure an analytic description of the dynamic process. Comparisons between the low-order model and unsteady computational fluid dynamics simulation results show the low-order model has the capability of qualitatively describing the bistability and hysteresis behaviors of shock motion.

Observations on the non-mixed length and unsteady shock motion in a two dimensional supersonic ejector

Key features that drive the operation of a supersonic ejector are the complex gasdynamic interactions of the primary and secondary flows within a variable area duct and the phenomenon of compressible turbulent mixing between them, which have to be understood at a fundamental level. An experimental study has been carried out on the mixing characteristics of a two dimensional supersonic ejector with a supersonic primary flow (air) of Mach number 2.48 and the secondary flow (subsonic) which is induced from the ambient. The non-mixed length, which is the length within the ejector for which the primary and secondary flow remain visually distinct is used to characterize the mixing in the ejector. The operating pressures, flow rates and wall static pressures along the ejector have been measured. Two flow visualization tools have been implemented—time resolved schlieren and laser scattering flow visualization. An important contribution has been the development of in-house image processing algorithms on the MATLAB platform to detect the non-mixed length from the schlieren and laser scattering images. The ratio of mass flow rates of the secondary flow to primary flow (entrainment ratio) has been varied in a range of 0.15–0.69 for two locations of the primary nozzle in the ejector duct. Representative cases have been computed using commercial CFD tool (Fluent) to supplement the experiments. Significant outcomes of the study are—the non-mixed length quantified from the flow visualization images is observed to lie within 4.5 to 5.2 times the height of the mixing duct which is confirmed by the wall static pressure profiles. The flow through the supersonic ejector in the mixed regime is explained using corroborative evidences from different diagnostic tools. A reduction of the non-mixed length by 46.7% is observed at operating conditions when the nozzle is sufficiently overexpanded. The disturbance caused to the mixing layer due to unsteady shock-boundary layer interactions within the nozzle at such conditions enhances mixing. The analysis of time resolved schlieren images have provided interesting observations on repetitive back and forth motion of the shock cells in the primary flow with a co-flowing secondary flow in the confines of the supersonic ejector. The oscillations have significant amplitudes (order of the nozzle height) at the centerline. The details of these experiments followed by the analysis of data and the inferences drawn from the results are discussed in this article.

Effect of Angle Of Attack on Stiffness Derivative of an Oscillating Supersonic Delta Wing with Curved Leading Edges

In the Present paper effect of angle of incidence on Stiffness derivative of a delta wing with Curved leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which strips at different span wise location are independent of each other. This combines with similitude to give a piston theory which gives closed form solutions for stiffness derivatives at low supersonic to high supersonic Mach numbers. From the results it is seen that with the increase in the Mach number, there is a continuous decrease in the magnitude of stiffness derivatives for all the Mach number tested, however, the magnitude of decrement for different inertia level will differ. It is seen that with the increase in the angle of attack the stiffness derivative increases linearly, nevertheless, this linear behavior limit themselves for different Mach numbers. For Mach number M = 2, this limiting value of validity is fifteen degrees, for Mach 2.5 & 3, it is twenty five degrees, whereas, for Mach 3.5 & 4 it becomes thirty five degrees, when these stability derivatives were considered at various pivot positions; namely at h = 0.0, 0.4, 0.6, and 1.0. After scanning the results it was observed that with the shift of the pivot position from the leading edge to the trailing edge, the magnitude of stiffness and the damping derivatives continue to decrease progressively. Results have been obtained for supersonic flow of perfect gases over a wide range of angle of attack and Mach number. The effect of real gas, leading edge bluntness of the wing, shock motion, and secondary wave reflections are neglected.

Effect of Angle of attack on Stability Derivatives of a Delta wing in Hypersonic Flow with Straight leading edge

In the present paper effect of angle of attack on stability derivatives in pitch of delta wing for the attached shock case is been studied. A strip theory is used in which strips at different span-wise locations are independent. This combines with the similitude to give a piston theory. In the present theory, the similitude, and the piston theory have been extended to a flat wing with straight leading edges. The linear dependence of the stiffness derivative is seen for all parameters of the present study, however for higher angle of attack the nonlinearity in the stiffness derivative is observed; since at very high angle of attack the flow separation will take place. It is also, observed that when angle of attack is small the variation in the stiffness and damping derivative in pitch remains in the range around thirty to thirty six percent, later for higher angles of attack, namely ten to twenty five degrees this variation in the stiffness and damping derivatives is in the range from ten to fifteen percent; and for angles of attack beyond twenty five degrees it remains independent of angle of attack in spite of variations in the Mach number and angles of attack. When the stiffness and damping derivatives are considered for h = 0.6 which; is also happens to be the center of pressure and for some cases the aerodynamic center the independency with angle of attack has been observed. The present theory is valid for large angle of incidence and Mach number. The present theory is simpler than both Lui and Hui and Hui et al and brings out explicit dependence of the stability derivatives on the similarity parameter. The present theory is not valid for a detached shock case. Future research can be done by taking into account the effects of shock motion, viscosity, wave reflections and the real gas effects.

Application of a shock-fitted spectral collocation method for computing transient high-speed inviscid flows over a blunt nose

Interaction of freestream disturbances with high-speed inviscid flow over a blunt nose is simulated utilizing a shock-fitted spectral collocation method. The unsteady flow computations are made through solving the 2D Euler equations by virtue of such a dissipation-free numerical algorithm for precise unsteady flow simulations. A shock-fitting technique is employed to accurately compute the unsteady shock motions and its interaction with monochromatic freestream disturbances of different conditions. A symmetry condition is proposed to accurately model the both steady and unsteady characters of the symmetry boundary, which allows the use of halved geometries and avoids the extra computational cost. The computational results for a cylinder at Mach 8.03 are presented and verified through comparisons with other numerical and promising analytical solutions. The stagnation line where the most energetic interactions take place is inspected carefully. The study shows the significant influence of the shock on its subsequent flow field in unsteady simulations and notable ability of the shock-fitted spectral collocation method implemented for the study of such problems.

Development of a Double Beam Model for Predicting Intrusion in Pipelines

This paper examines pipeline safety and develops a mathematical model for predicting illegal intrusion. The model idealizes a typical pipeline structure as a pipe-in-pipe double beam, consisting of the process pipe encased in a larger diameter outer carrier pipe resting on an elastic soil foundation. Intrusion is considered to consist of hammering and cutting activities on the casing pipe which transmits shock motion to the process pipe. From the solution feedback control algorithms have been proposed for designing surveillance instruments which assist in mitigating the problem of illegal intrusion for harvesting of crude oil. A point sensor was used to simulate the response to intrusive hammering action induced on the casing pipe in a 2 m segment of the process pipe in an example. Sensor was conFigureured to measure displacement response at intervals of 2 seconds at (0.00, 0.06, 0.12,..., 2.00) m sampling points. The displacements indicated within the model assumption of zero damping, were 4.62 x 10-4 m and 4.24 x 10-4 m at the left and right hand anchors. A deflection of around-2.67 x 10-4 m was obtained at 0.94 m.