Showing papers on "Oblique shock published in 2010"

Applied Gas Dynamics

Abstract: Preface. About the Author. 1 Basic Facts. 1.1 Definition of Gas Dynamics. 1.2 Introduction. 1.3 Compressibility. 1.4 Supersonic Flow What is it? 1.5 Speed of Sound. 1.6 Temperature Rise. 1.7 Mach Angle. 1.8 Thermodynamics of Fluid Flow. 1.9 First Law of Thermodynamics (Energy Equation). 1.10 The Second Law of Thermodynamics (Entropy Equation). 1.11 Thermal and Calorical Properties. 1.12 The Perfect Gas. 1.13 Wave Propagation. 1.14 Velocity of Sound. 1.15 Subsonic and Supersonic Flows. 1.16 Similarity Parameters. 1.17 Continuum Hypothesis. 1.18 Compressible Flow Regimes. 1.19 Summary. Exercise Problems. 2 Steady One-Dimensional Flow. 2.1 Introduction. 2.2 Fundamental Equations. 2.3 Discharge from a Reservoir. 2.4 Streamtube Area Velocity Relation. 2.5 de Laval Nozzle. 2.6 Supersonic Flow Generation. 2.7 Performance of Actual Nozzles. 2.8 Diffusers. 2.9 Dynamic Head Measurement in Compressible Flow. 2.10 Pressure Coefficient. 2.11 Summary. Exercise Problems. 3 Normal Shock Waves. 3.1 Introduction. 3.2 Equations of Motion for a Normal Shock Wave. 3.3 The Normal Shock Relations for a Perfect Gas. 3.4 Change of Stagnation or Total Pressure Across a Shock. 3.5 Hugoniot Equation. 3.6 The Propagating Shock Wave. 3.7 Reflected Shock Wave. 3.8 Centered Expansion Wave. 3.9 Shock Tube. 3.10 Summary. Exercise Problems. 4 Oblique Shock and ExpansionWaves. 4.1 Introduction. 4.2 Oblique Shock Relations. 4.3 Relation between and . 4.4 Shock Polar. 4.5 Supersonic Flow Over a Wedge. 4.6 Weak Oblique Shocks. 4.7 Supersonic Compression. 4.8 Supersonic Expansion by Turning. 4.9 The Prandtl Meyer Expansion. 4.10 Simple and Nonsimple Regions. 4.11 Reflection and Intersection of Shocks and Expansion Waves. 4.12 Detached Shocks. 4.13 Mach Reflection. 4.14 Shock-Expansion Theory. 4.15 Thin Aerofoil Theory. 4.15.1 Application of Thin Aerofoil Theory. 4.16 Summary. Exercise Problems. 5 Compressible Flow Equations. 5.1 Introduction. 5.2 Crocco's Theorem. 5.3 General Potential Equation for Three-Dimensional Flow. 5.4 Linearization of the Potential Equation. 5.5 Potential Equation for Bodies of Revolution. 5.6 Boundary Conditions. 5.7 Pressure Coefficient. 5.8 Summary. Exercise Problems. 6 Similarity Rule. 6.1 Introduction. 6.2 Two-Dimensional Flow: The Prandtl-Glauert Rule for Subsonic Flow. 6.3 Prandtl Glauert Rule for Supersonic Flow: Versions I and II. 6.4 The von Karman Rule for Transonic Flow. 6.5 Hypersonic Similarity. 6.6 Three-Dimensional Flow: Gothert s Rule. 6.7 Summary. Exercise Problems. 7 Two-Dimensional Compressible Flows. 7.1 Introduction. 7.2 General Linear Solution for Supersonic Flow. 7.3 Flow Over a Wave-Shaped Wall. 7.4 Summary. Exercise Problems. 8 Flow with Friction and Heat Transfer. 8.1 Introduction. 8.2 Flow in Constant Area Duct with Friction. 8.4 Flow with Heating or Cooling in Ducts. 8.5 Summary. Exercise Problems. 9 Method of Characteristics. 9.1 Introduction. 9.2 The Concepts of Characteristic. 9.3 The Compatibility Relation. 9.4 The Numerical Computational Method. 9.5 Theorems for Two-Dimensional Flow. 9.6 Numerical Computation with Weak Finite Waves. 9.7 Design of Supersonic Nozzle. 9.8 Summary. 10 Measurements in Compressible Flow. 10.1 Introduction. 10.2 Pressure Measurements. 10.3 Temperature Measurements. 10.4 Velocity and Direction. 10.5 Density Problems. 10.6 Compressible Flow Visualization. 10.7 Interferometer. 10.8 Schlieren System. 10.9 Shadowgraph. 10.10 Wind Tunnels. 10.11 Hypersonic Tunnels. 10.12 Instrumentation and Calibration of Wind Tunnels. 10.13 Calibration and Use of Hypersonic Tunnels. 10.14 Flow Visualization. 10.15 Summary. Exercise Problems. 11 Ramjet. 11.1 Introduction. 11.2 The Ideal Ramjet. 11.3 Aerodynamic Losses. 11.4 Aerothermodynamics of Engine Components. 11.5 Flow Through Inlets. 11.6 Performance of Actual Intakes. 11.7 Shock Boundary Layer Interaction. 11.8 Oblique Shock Wave Incident on Flat Plate. 11.9 Normal Shocks in Ducts. 11.10 External Supersonic Compression. 11.11 Two-Shock Intakes. 11.12 Multi-Shock Intakes. 11.13 Isentropic Compression. 11.14 Limits of External Compression. 11.15 External Shock Attachment. 11.16 Internal Shock Attachment. 11.17 Pressure Loss. 11.18 Supersonic Combustion. 11.19 Summary. 12 Jets. 12.1 Introduction. 12.2 Mathematical Treatment of Jet Profiles. 12.3 Theory of Turbulent Jets. 12.4 Experimental Methods for Studying Jets and the Techniques Used for Analysis. 12.5 Expansion Levels of Jets. 12.6 Control of Jets. 12.7 Summary. Appendix. References. Index.

Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation

Abstract: The interaction of a normal shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number M∞ = 1.3 and Reynolds number Reθ ≈ 1200 (based on the momentum thickness of the upstream boundary layer) is analysed by means of direct numerical simulation of the compressible Navier–Stokes equations. The computational methodology is based on a hybrid linear/weighted essentially non-oscillatory conservative finite-difference approach, whereby the switch is controlled by the local regularity of the solution, so as to minimize numerical dissipation. As found in experiments, the mean flow pattern consists of an upstream fan of compression waves associated with the thickening of the boundary layer, and the supersonic region is terminated by a nearly normal shock, with substantial bending of the interacting shock. At the selected conditions the flow does not exhibit separation in the mean. However, the interaction region is characterized by ‘intermittent transitory detachment’ with scattered spots of instantaneous flow reversal throughout the interaction zone, and by the formation of a turbulent mixing layer, with associated unsteady release of vortical structures. As found in supersonic impinging shock interactions, we observe a different amplification of the longitudinal Reynolds stress component with respect to the others. Indeed, the effect of the adverse pressure gradient is to reduce the mean shear, with subsequent suppression of the near-wall streaks, and isotropization of turbulence. The recovery of the boundary layer past the interaction zone follows a quasi-equilibrium process, characterized by a self-similar distribution of the mean flow properties.

Velocimetry measurements of unstart in an inlet-isolator model in Mach 5 flow

Abstract: The dynamics of unstart in a floor-mounted inlet-isolator model in a Mach 5 flow are investigated experimentally using particle image velocimetry and fast-response wall pressure measurements The inlet compression is obtained with a 6-deg ramp and the isolator is a rectangular straight duct that is 254 mm high by 508 mm wide by 2423 mm long Unstart is initiated from the scramjet mode (fully supersonic in the isolator) by deflecting a motorized flap at the downstream end of the isolator With the flap fully down, the particle image velocimetry data of the started flow capture the characteristics of the isolator boundary layers and the initial inlet reflected shock system During unstart, the unstart shock system propagates upstream through the inlet-isolator The particle image velocimetry data reveal a complex, three-dimensional flow structure that is strongly dependent on viscous mechanisms Particularly, the unstart shock system propagates upstream and induces significant boundary-layer separation Side-view particle image velocimetry data show that the locations of strongest separation during unstart correlate with the impingement locations of the initial inlet shock as it reflects down the isolator For example, in the middle of unstart, the unstart shock system is associated with massive separation of the ceiling boundary layer that begins where the first inlet shock reflection impinges on the ceiling The observation that separation increases at the inlet shock reflection impingement locations is likely due to the fact that the boundary layers in these locations are subject to larger adverse pressure gradients, thus making them more susceptible to separation During the unstart process, large regions of separated flow form near the floor and ceiling with reverse flow velocities up to about 04U ∞ These regions of separated, subsonic flow appear to extend to the isolator exit, creating a path by which the isolator exit boundary condition can be communicated upstream Plan-view particle image velocimetry data show the unstart process begins with separation of the isolator sidewall boundary layers Overall, the unstart flow structure is highly three-dimensional

Numerical simulations of effects of micro vortex generators using immersed-boundary methods

Abstract: This work presents an immersed-boundary technique for compressible, turbulent flows and applies the technique to simulate the effects of micro vortex generators in controlling oblique-shock/turbulent boundary-layer interactions. The Reynolds-averaged Navier-Stokes equations, closed using the Menter k-ω turbulence model, are solved in conjunction with the immersed-boundary technique. The approach is validated by comparing solutions obtained using the immersed-boundary technique with solutions obtained on a body-fitted mesh and with experimental laser Doppler anemometry data collected at Cambridge University for Mach 2.5 flow over single micro vortex generators. Simulations of an impinging oblique-shock boundary-layer interaction at Mach 2.5 with and without micro vortex-generator flow control are also performed, considering the development of the flow in the entire wind tunnel. Comparisons are made with experimental laser Doppler anemometry data and surface-pressure measurements from Cambridge University and an analysis of the flow structure is performed. The results show that three dimensional effects initiated by the interaction of the oblique shock with the sidewall boundary layers significantly influence the flow patterns in the actual experiment. The general features of the interactions with and without the micro vortex-generator array are predicted to good accord by the Reynolds-averaged Navier-Stokes/ immersed-boundary model.

First complete determination of plasma physical parameters across a coronal mass ejection-driven shock

Abstract: We report on the study of a fast coronal mass ejection (CME)-driven shock associated with the solar eruption of 2002 March 22. This event was observed in the intermediate corona both in white light and the extreme ultraviolet (EUV) by the LASCO and UVCS instruments on board the Solar and Heliospheric Observatory ,a s well as in metric and decametric wavelengths through space- and ground-based radio observatories. Clear signatures of shock transit are (1) strong type II emission lanes observed after the CME initiation, (2) strong Ovi λλ1032, 1037 line profile broadenings (up to ∼2 × 10 7 K) associated with the shock transit across the UVCS slit field of view, and (3) a density enhancement located in LASCO images above the CME front. Since the UVCS slit was centered at 4.1 R� , in correspondence with the flank of the expanding CME, this observation represents the highest UV detection of a shock obtained so far with the UVCS instrument. White-light and EUV data have been combined in order to estimate not only the shock compression ratio and the plasma temperature, but also the strength of the involved coronal magnetic fields, by applying the Rankine–Hugoniot equations for the general case of oblique shocks. Results show that, for a compression ratio X = 2.06 as derived from LASCO data, the coronal plasma is heated across the shock from an initial temperature of 2.3 × 10 5 Ku p to 1.9 × 10 6 K, while at the same time the magnetic field undergoes a compression from a pre-shock value of ∼0.02 G up to a post-shock field of ∼0.04 G. Magnetic and kinetic energy density increases at the shock are comparable (in agreement with the idea of equipartition of energy), and both are more than two times larger than the thermal energy density increase. This is the first time that a complete characterization of pre- and post-shock plasma physical parameters has been derived in the solar corona.

Effect of air jet vortex generators on a shock wave boundary layer interaction

Abstract: The effect of upstream injection by means of continuous air jet vortex generators (AJVGs) on a shock wave turbulent boundary layer interaction is experimentally investigated. The baseline interaction is of the impinging type, with a flow deflection angle of 9.5degrees and a Mach number Me = 2.3. Considered are the effects of the AJVGs on the upstream boundary layer flow topology and on the spatial and dynamical characteristics of the interaction. To this aim, Stereoscopic Particle Image Velocimetry has been employed, in addition to hot-wire anemometry (HWA) for the investigation of the unsteady characteristics of the reflected shock. The AJVGs cause a reduction of the separation bubble length and height. In addition, the energetic frequency range of the reflected shock is increased by approximately 50%, which is in qualitative agreement with the smaller separation bubble size.

Numerical investigation of the compressible flow past an aerofoil

Abstract: Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M? = 0.76 and a Reynolds number Re = 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.

Microramps Upstream of an Oblique-Shock/Boundary-Layer Interaction

Abstract: To examine the potential of micro vortex generators for shock/boundary-layer interaction control, a detailed experimental and computational study in a supersonic boundary layer at M = 3.0 was undertaken. The experiments employed a flat-plate boundary layer with an impinging oblique shock with downstream total-pressure measurements. The moderate Reynolds number of 3800 allowed the computations to use monotone-integrated large eddy simulations. The monotone-integrated large eddy simulations predictions indicated that the shock changes the structure of the turbulent eddies and the primary vortices generated from the microramp. Furthermore, they generally reproduced the experimentally obtained mean velocity profiles, unlike similarly resolved Reynolds-averaged Navier-Stokes computations. The experiments and monotone-integrated large eddy simulations results indicate that the microramps, for which the height is h ≈ 0.5δ, can significantly reduce boundary-layer thickness and improve downstream boundary-layer health as measured by the incompressible shape function H. Regions directly behind the ramp centerline tended to have increased boundary-layer thickness, indicating the significant three-dimensionality of the flowfield. Compared with baseline sizes, smaller microramps yielded improved total-pressure recovery. Moving the smaller ramps closer to the shock interaction also reduced the displacement thickness and the separated area. This effect is attributed to decreased wave drag and the closer proximity of the vortex pairs to the wall.

Generation of cylindrical converging shock waves based on shock dynamics theory

Abstract: A simple but effective technique is proposed to generate cylindrical converging shock waves. The shock dynamics is employed to design a curved wall profile of the test section in a shock tube. When a planar shock wave propagates forward along the curved wall, the disturbances produced by the curved wall would continuously propagate along the shock surface and bend the shock wave. As an example, the wall profile for an incident shock Mach number of M0=1.2 and a converging angle of 15° is tested numerically and experimentally. Both numerical and experimental results show a perfect circular shock front, which validates our method.

Experimental investigation on the shock-wave load attenuation by geometrical means

Abstract: The pressures and loads induced on the center of the end-wall of a shock tube by a shock wave that passes through different types of obstacles are investigated. Efforts have been made to understand the effect of the obstacle geometry on the load development. The experiments were conducted in a shock tube apparatus in which a modular test section was implemented. It is found that for a single-obstacle setup, the effect of the geometry becomes dominant when the blockage ratio (i.e., the ratio of the non-open area to the overall cross section) is large. It is also found that the attenuation effect is more pronounced for general geometries, which form diverging-like nozzle. In the case of multi-obstacles geometry, the same sensitivity to the blockage ratio as in the single-obstacle case is found. However, amplification or attenuation of the shock-wave load on the center of the end-wall of a shock tube is observed when the number of the obstacles is increased. This is due to different trapping effects of the shock wave between the obstacle and the end-wall.

Behavior of shock trains in a diverging duct

Abstract: A shock train inside a diverging duct is analyzed at different pressure levels and Mach numbers. Nonreactive pressurized cold gas is used as fluid. The structure and pressure recovery inside the shock train is analyzed by means of wall pressure measurements, Schlieren images and total pressure probes. During the course of the experiments, the total pressure of the flow, the back pressure level and the Mach number upstream of the compression region have been varied. It is shown that the Reynolds number has some small effect on the shock position and length of the shock train. However, more dominant is the effect of the confinement level and Mach number. The results are compared with analytical and empirical models from the literature. It was found that the empirical pseudo-shock model from Billig and the analytical mass averaging model from Matsuo are suitable to compute the pressure gradient along the shock train and total pressure loss, respectively.

Statistical study of the quasi-perpendicular shock ramp widths

Abstract: [1] The width of the collisionless shock front is one of the key shock parameters. The width of the main shock transition layer is related to the nature of the collisionless process that balances nonlinearity and therefore leads to the formation of the shock itself. The shock width determines how the incoming plasma particles interact with the macroscopic fields within the front and, therefore, the processes that result in the energy redistribution at the front. Cluster and Themis measurements at the quasi-perpendicular part of the terrestrial bow shock are used to study the spatial scale of the magnetic ramp. It is shown that statistically the ramp spatial scale decreases with the increase of the shock Mach number. This decrease of the shock scale together with previously observed whistler packets in the foot of supercritical quasi-perpendicular shock indicates that it is the dispersion that determines the size of magnetic ramp even for supercritical shocks.

Unsteadiness in shock-wave/boundary layer interactions

Abstract: The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. This work investigates the interaction between an impinging oblique shock and a supersonic turbulent boundary layer via large-eddy simulations. Special care is taken at the inlet in order to avoid introducing artificial low-frequency modes that could affect the interaction. All simulations cover extensive integration times to allow for a spectral analysis at the low frequencies of interest. The simulations bring clear evidence of the existence of broadband and energetically-significant low-frequency oscillations in the vicinity of the reflected shock, thus confirming earlier experimental findings. Furthermore, these oscillations are found to persist even if the upstream boundary layer is deprived of long coherent structures. 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 reflectedshock foot low-frequency motions is derived. This model is applied to a wide range of input parameters. 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. Under some assumptions, the coupling between the shock and the boundary layer is mathematically equivalent to a first-order low-pass filter. Therefore, it is argued that the observed lowfrequency unsteadiness is not necessarily a property of the forcing, either from upstream or downstream of the shock, but simply an intrinsic property of the coupled dynamical system.

Propagation of a strong cylindrical shock wave in a rotational axisymmetric dusty gas with exponentially varying density

Abstract: Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas, which has a variable azimuthal and axial fluid velocity. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The equilibrium flow conditions are assumed to be maintained, and the density of the mixture is assumed to be varying and obeying an exponential law. The fluid velocities in the ambient medium are assumed to obey exponential laws. The shock wave moves with variable velocity. The effects of variation of the mass concentration of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times. Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made.

Microramp Flow Control of Normal Shock/Boundary-Layer Interactions

Abstract: Boundary-layer bleed has conventionally been used to control separation due to shock wave/boundary-layer interactions within supersonic engine inlets. However, bleed systems result in a loss of captured mass flow, incurring higher drag and, ultimately, lower propulsion system efficiency. Microramp sub-boundary-layer vortex generators arranged in a spanwise array have been proposed in the past as a form of flow-control methodology for shock wave/ boundary-layer interactions. Experiments have been conducted herein at Mach 1.4 to characterize flow details of such devices and obtain quantitative measurements of their ability to control the interaction of a normal shock with a turbulent boundary layer. The flowfield was analyzed using schlieren photography, surface oil flow visualization, pressure-sensitive paint, and particle image velocimetry. An array of three microramps, for which the height was scaled to 36% of the incoming boundary-layer thickness, was placed ahead of the normal shock interaction. It was demonstrated that the microramps did entrain higher-momentum fluid into the boundary layer, which improved boundary-layer health. Specifically, the incompressible displacement thickness, momentum thickness, and shape factor were decreased, and the skin friction coefficient was increased, for the shock wave/boundary-layer interaction with the microramp array relative to the no-array case.

Molecular Weight and Shock-Wave Effects on Transverse Injection in Supersonic Flow

Abstract: An experimental study of the effects of injectant molecular weight on transverse-jet mixing in a supersonic crossflow is reported. In addition, the effects of an oblique shock impinging near the injection station were investigated. The examined gaseous injector is circular in geometry and angled downstream at 30 deg to the horizontal. Test conditions involved sonic injection of helium, methane, and air at a jet-to-freestream momentum flux ratio of 2.1 into a nominal Mach 4 air cross stream with average Reynolds number 5.77e + 7 per meter to provide a range of injectant molecular weights from 4―29. Sampling probe measurements were used to determine the local helium and methane concentration. A miniature five-hole pressure probe, pitot and cone-static pressure probes, and a diffuser-thermocouple probe were employed to document the flow. The goals of this effort are twofold. The first goal is to broaden and enrich the database for transverse injection in high-speed flows. Second, these data will aid greatly in the development of advanced turbulence models with a wide range of applicability for high-speed mixing flows. The main experimental results showed that an impinging shock reduces penetration and increases mixing for injectants of all molecular weights. Higher molecular weight injectant seems to increase penetration, but the effect is weak. The effects of shock impingement were strongest when this occurred downstream of, and closest to, the injection port.

Understanding large SEP events with the PATH code: Modeling of the 13 December 2006 SEP event

Abstract: The Particle Acceleration and Transport in the Heliosphere (PATH) numerical code was developed to understand solar energetic particle (SEP) events in the near-Earth environment. We discuss simulation results for the 13 December 2006 SEP event. The PATH code includes modeling a background solar wind through which a CME-driven oblique shock propagates. The code incorporates a mixed population of both flare and shock-accelerated solar wind suprathermal particles. The shock parameters derived from ACE measurements at 1 AU and observational flare characteristics are used as input into the numerical model. We assume that the diffusive shock acceleration mechanism is responsible for particle energization. We model the subsequent transport of particles originated at the flare site and particles escaping from the shock and propagating in the equatorial plane through the interplanetary medium. We derive spectra for protons, oxygen, and iron ions, together with their time-intensity profiles at 1 AU. Our modeling results show reasonable agreement with in situ measurements by ACE, STEREO, GOES, and SAMPEX for this event. We numerically estimate the Fe/O abundance ratio and discuss the physics underlying a mixed SEP event. We point out that the flare population is as important as shock geometry changes during shock propagation for modeling time-intensity profiles and spectra at 1 AU. The combined effects of seed population and shock geometry will be examined in the framework of an extended PATH code in future modeling efforts.

Simulation of Shock/Boundary-Layer Interactions with Bleed Using Immersed-Boundary Methods

Abstract: This work utilizes an immersed boundary (IB) method to simulate the effects of arrays of discrete bleed ports in controlling shock wave / turbulent boundary layer inter actions . Both Reynolds averaged Navier -Stokes (RANS) and hybrid large -eddy / Reynolds -averaged Navier -Stokes (LES/RANS) turbulence closures are used with the IB technique. The approach is validated by conducting simulations of Mach 2.5 flow over a perfo rated plate containing 18 individual bleed holes. Predictions of discharge coefficient as a function of bleed plenum pressure are compared with experimental data. Simulations of an impinging oblique shock / boundary layer interaction at Mach 2.45 with an d without active bleed control are also performed. The 68 -hole bleed plate is rendered as an immersed object in the computational domain. Wall pressure predictions show that, in general, the LES/RANS technique under -estimate s the upstream extent of axi al separation that occurs in the absence of bleed. Good agreement with P itot -pressure surveys throughout the interaction region is obtained, however. Active suction completely removes the separation region and induces local disturbances in the wall pres sure distributions that are associated with the expansion of the boundary layer fluid into the bleed port and its subsequ ent re -compression. Predicted Pitot -pressure distributions are in good agreement with experiment for the case with bleed. Swirl stre ngth probability -density distributions are used to estimate the evolution of turbulence length -sca les throughout the interaction, and the effects of bleed on the amplification of Reynolds stresses are highlighted. Finally, simple improvements to engineerin g-level bleed models are proposed based on the computational results.

Shock wave configurations and flow structures in non-axisymmetric underexpanded sonic jets

Abstract: An experimental and numerical study of underexpanded free sonic jet flows issuing from rectangular, elliptical and slot nozzles has been undertaken. Aspect ratios (AR) of 1, 2, and 4 are described at pressure ratios (exit plane pressure to ambient pressure), of 2 and 3. There is good qualitative agreement between the experimental observations and the numerical predictions. In the case of rectangular jets, a complex system of shock waves forming the incident shock system is identified. This shock wave system originates at the corners of the nozzle exits, and proceeds downstream. Mach reflections are found to occur on the incident shock wave surface as well as the presence of a Mach disk terminating the first jet cell. This Mach disk has the shape of a square, a hexagon, or an octagon depending on the nozzle shape. For slot and elliptical jets, the formation of the incident shock wave was not observed along the minor axis plane of the nozzle for AR > 2. The incident shock wave was observed to originate downstream of the nozzle exit in the major axis plane. This wave system undergoes a transition to Mach reflection as it propagates downstream of the nozzle exit. In all cases tested, the shape of the jet boundary is significantly distorted. In rectangular jets, the narrowing of the jet boundary along the diagonal axis of the nozzle exit is observed, and in the case of the elliptical and slot jets axis switching is noted.

Research on the mechanics of underwater supersonic gas jets

Abstract: An experimental research was carried out to study the fluid mechanics of underwater supersonic gas jets. High pressure air was injected into a water tank through converging-diverging nozzles (Laval nozzles). The jets were operated at different conditions of over-, full- and under-expansions. The jet sequences were visualized using a CCD camera. It was found that the injection of supersonic air jets into water is always accompanied by strong flow oscillation, which is related to the phenomenon of shock waves feedback in the gas phase. The shock wave feedback is different from the acoustic feedback when a supersonic gas jet discharges into open air, which causes screech tone. It is a process that the shock waves enclosed in the gas pocket induce a periodic pressure with large amplitude variation in the gas jet. Consequently, the periodic pressure causes the jet oscillation including the large amplitude expansion. Detailed pressure measurements were also conducted to verify the shock wave feedback phenomenon. Three kinds of measuring methods were used, i.e., pressure probe submerged in water, pressure measurements from the side and front walls of the nozzle devices respectively. The results measured by these methods are in a good agreement. They show that every oscillation of the jets causes a sudden increase of pressure and the average frequency of the shock wave feedback is about 5–10 Hz.

Large-Eddy Simulation of an Oblique Shock Impinging on a Turbulent Boundary Layer

Abstract: Large-eddy simulation (LES) of an oblique shock impinging on a supersonic turbulent boundary layer is carried out with a high-order compact differencing scheme using localized artificial diffusivity (LAD) for shock capturing. Flow conditions attempt to match those of the tomographic particle image velocimetry (PIV) experiments conducted at the Delft University of Technology (M∞ = 2.05 and φ = 8°). However, due to computational cost, the Reynolds number is taken to be Reδ = 20,000 (1/30 th of the experimental Reynolds number), and an attempt is made to geometrically match the interaction parameters. Inflow conditions are generated by an improved recycling/rescaling method to eliminate the non-physical “tones” associated with standard recycling/rescaling. The numerical scheme is first validated by simulating a two-dimensional laminar shock wave / boundary layer interaction (SWBLI). Next, a three-dimensional simulation with progressive mesh refinement is conducted to investigate flow physics and establish confidence in the ability of the computational method to accurately and efficiently simulate complex supersonic flow phenomena. Mean and fluctuating profiles of velocity, pressure, and skin friction provide good indication of grid convergence between the two highest levels of refinement. Instantaneous data fields are analyzed, and observations are made regarding “flapping” motion caused by boundary layer turbulence and spanwise variation in shock location. Additionally, the range of spatial and temporal scales captured by the present work is quantified by analyzing spanwise wavenumber and frequency spectra at various locations in the flow. Through analysis of the frequency spectra of the wall pressure signal, low-frequency motion of the separation bubble with a time scale ~O(100δ/u∞) is observed and described. Through direct comparison, we additionally observe that standard recycling/rescaling inflow conditions may result in different low-frequency behavior.

Instability of shock-induced nozzle flow separation

Abstract: 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.

On the scaling and unsteadiness of shock induced separation

Abstract: Shock wave boundary layer interactions (SWBLI) are a common phenomenon in transonic and supersonic flows. The presence of shock waves, induced by specific geometrical configurations, causes a rapid increase of the pressure, which can lead to flow separation. Examples of such interactions are found in amongst others rocket engine nozzles and on aerospikes, on re-entry vehicles, in supersonic and hypersonic engine intakes, and at the tips of compressor and turbine blades in jet engines. The interactions are important factors in vehicle development. Both the separated flow and the induced shock have been shown to be highly unsteady, causing pressure fluctuations and thermal loading. This generally leads to a degraded performance and possibly structural failure. The current work therefore aims to improve the physical understanding of the mechanisms that govern the interaction, with a special attention for the flow organisation and for the sources of the unsteadiness of the induced shock. In particular, the case of a reflecting incident shock is investigated, but the results find their application more generally in other configurations. Additionally, it is verified whether the interaction can be controlled by means of upstream fluid injection. To attain these aims, experiments were performed, comparing systematically several interactions for a range of shock intensities (producing incipiently separated and well separated flows) and under a number of flow conditions (Mach numbers of 1.7 and 2.3 and Reynolds numbers of 5,000 (‘low’) and 50,000 (‘high’)). This was done using the latest developments in the field of measurement techniques. A large amount of data was obtained for multiple interactions by means of a range of flow diagnostic techniques, yielding highly consistent results. A full field determination of the characteristic time scales by means of dual plane particle image velocimetry (Dual-PIV) has shown that the unsteadiness frequencies in the high Reynolds number incipient interaction span almost three orders of magnitude, demonstrating additionally the existence of low frequency dynamics of the reflected shock. The effect of control by means of air jet vortex generators (AJVGs) was thoroughly characterised, putting in evidence the generation of pairs of counter-rotating vortices of unequal strength that induce streaks of low and high speed fluid. These in their turn modify the separation bubble size without suppressing it. There is an inversely proportional relation between the reflected shock frequency and the bubble size. A scaling analysis was made, aimed at reconciling the observed discrepancies between interactions documented in literature. As part of this analysis, a separation criterion has been formulated that depends on the free-stream Mach number and the flow deflection angle only. In addition, a scaling approach has been derived for the interaction length based on the mass and momentum conservation. A conditional analysis has been performed based on the instantaneous separation bubble size. The generation and successive shedding of large coherent structures was found to be present also in absence of instantaneous flow separation. For the incipient cases, a link has been put into evidence between the separation region and the state of the upstream boundary layer. For the separated interactions, this link was absent and the shock unsteadiness seems to be mainly related to the separation bubble pulsation. The separation criterion in combination with the normalised interaction length represents a single trend line onto which all data for a large scope of documented interactions fall together with only a moderate scatter. This trend line predicts that the only way to effectively eliminate a separation bubble (without massive separation) by means of upstream control is by decreasing the displacement thickness of the incoming boundary layer. A scaling for the wall normal coordinate has been defined based on the interaction length with a correction for Mach number effects, producing a large resemblance in the geometric organisation of the mean and turbulent flow fields within the considered interactions. It can be concluded that multiple unsteadiness mechanisms are at work within the interaction, irrespective of the Mach number and the Reynolds number. It is proposed that the relative importance of the different mechanisms shifts with the imposed shock intensity. It seems that weak interactions without instantaneous flow separation should be governed by upstream effects only, with rather high shock frequencies. For incipient interactions, downstream effects start to occur; the region of high turbulence intensities displays mainly a lifting motion, producing a shock foot of varying strength and a shock unsteadiness that involves a time scales which can differ by at least one decade. Interactions with significant flow separation show mainly a translating motion, producing a low frequency unsteadiness and a shock foot of constant strength, which is in accordance with a free interaction behaviour. Concerning the Reynolds number and Mach number effects, it is concluded that for turbulent boundary layers, the onset of separation is Reynolds number independent. The interaction length is however governed by both the Reynolds number and the Mach number.

Intensification of shock-induced combustion by electric-discharge-excited oxygen molecules: numerical study

Abstract: Mechanisms of combustion enhancement in a supersonic H2–O2 reactive flow behind an oblique shock wave front are investigated when vibrational and electronic states of O2 molecule are excited by an electric discharge. The analysis is carried out on the base of updated thermally nonequilibrium kinetic model for the H2–O2 mixture combustion. The presence of vibrationally and electronically excited O2 molecules in the discharge-activated oxygen flow allows to intensify the chain mechanism and to shorten significantly the induction zone length at shock-induced combustion. It makes possible, for example, to ignite the atmospheric pressure H2–O2 mixture at the distance shorter than 1 m behind the weak oblique shock wave at a small energy Es = 1.2 × 10–2 J · cm–3 input to O2 molecules. At higher pressure it is needed to put greater specific energy into the gas in order to ignite the mixture at appropriate distances. It is shown that excitation of O2 molecules by electric discharge is much more effective for accel...

Micro-Ramps for External Compression Low-Boom Inlets

Abstract: The application of vortex generators for flow control in an external compression, axisymmetric, low-boom concept inlet was investigated using RANS simulations with three-dimensional (3-D), structured, chimera (overset) grids and the WIND-US code. The low-boom inlet design is based on previous scale model 1- by 1-ft wind tunnel tests and features a zero-angle cowl and relaxed isentropic compression centerbody spike, resulting in defocused oblique shocks and a weak terminating normal shock. Validation of the methodology was first performed for micro-ramps in supersonic flow on a flat plate with and without oblique shocks. For the inlet configuration, simulations with several types of vortex generators were conducted for positions both upstream and downstream of the terminating normal shock. The performance parameters included incompressible axisymmetric shape factor, separation area, inlet pressure recovery, and massflow ratio. The design of experiments (DOE) methodology was used to select device size and location, analyze the resulting data, and determine the optimal choice of device geometry. The optimum upstream configuration was found to substantially reduce the post-shock separation area but did not significantly impact recovery at the aerodynamic interface plane (AIP). Downstream device placement allowed for fuller boundary layer velocity profiles and reduced distortion. This resulted in an improved pressure recovery and massflow ratio at the AIP compared to the baseline solid-wall configuration.

3D model of bow shocks

Abstract: Context. Shocks produced by outflows from young stars are often observed as bow-shaped structures in which the H2 line strength and morphology are characteristic of the physical and chemical environments and the velocity of the impact. Aims. We present a 3D model of interstellar bow shocks propagating in a homogeneous molecular medium with a uniform magnetic field. The model enables us to estimate the shock conditions in observed flows. As an example, we show how the model can reproduce rovibrational H2 observations of a bow shock in OMC1.Methods. The 3D model is constructed by associating a planar shock with every point on a 3D bow skeleton. The planar shocks are modelled with a highly sophisticated chemical reaction network that is essential for predicting accurate shock widths and line emissions. The shock conditions vary along the bow surface and determine the shock type, the local thickness, and brightness of the bow shell. The motion of the cooling gas parallel to the bow surface is also considered. The bow shock can move at an arbitrary inclination to the magnetic field and to the observer, and we model the projected morphology and radial velocity distribution in the plane-of-sky. Results. The morphology of a bow shock is highly dependent on the orientation of the magnetic field and the inclination of the flow. Bow shocks can appear in many different guises and do not necessarily show a characteristic bow shape. The ratio of the H2 v = 2-1 S(1) line to the v = 1-0 S(1) line is variable across the flow and the spatial offset between the peaks of the lines may be used to estimate the inclination of the flow. The radial velocity comes to a maximum behind the apparent apex of the bow shock when the flow is seen at an inclination different from face-on. Under certain circumstances the radial velocity of an expanding bow shock can show the same signatures as a rotating flow. In this case a velocity gradient perpendicular to the outflow direction is a projection effect of an expanding bow shock lighting up asymmetrically because of the orientation of the magnetic field. With the 3D model we reproduce the brightness levels in three H2 lines as well as the shape and size of a chosen bow shock in OMC1. The inferred bow inclination and the orientation and strength of the magnetic field fit into the pattern suggested by independent observations.

Theory of radiative shocks in the mixed, optically thick-thin case

Abstract: A theory of radiating shocks that are optically thick in the downstream (postshock) state and optically thin in the upstream (preshock) state, which are called thick-thin shocks, is presented. Relations for the final temperature and compression, as well as the postshock temperature and compression as a function of the shock strength and initial pressure, are derived. The model assumes that there is no radiation returning to the shock from the upstream state. Also, it is found that the maximum compression in the shock scales as the shock strength to the 1/4 power. Shock profiles for the material downstream of the shock are computed by solving the fluid and radiation equations exactly in the limit of no radiation returning to the shock. These profiles confirm the validity and usefulness of the model in that limit.

Shock Waves in Dynamic Cavity Expansion

Abstract: High velocity cavitation fields are investigated in the context of large strain J 2 plasticity with strain hardening and elastic compressibility. The problem setting is that of an internally pressurized spherical cavity, embedded in an unbounded medium, which grows spontaneously with constant velocity and pressure. Expansion velocity is expected to be sufficiently high to induce a plastic shock wave, hardly considered in earlier dynamic cavitation studies. Jump conditions across singular spherical surfaces (shock waves) are fully accounted for and numerical illustrations are provided over a wide range of power hardening materials. Simple formulae are derived for shock wave characteristics and for the asymptotic behavior within near cavity wall boundary layer.