Showing papers on "Oblique shock published in 2002"

Dynamical Simulations of Magnetically Channeled Line-driven Stellar Winds. I. Isothermal, Nonrotating, Radially Driven Flow

Abstract: We present numerical magnetohydrodynamic (MHD) simulations of the effect of stellar dipole magnetic fields on line-driven wind outflows from hot, luminous stars. Unlike previous fixed-field analyses, the simulations here take full account of the dynamical competition between field and flow and thus apply to a full range of magnetic field strength and within both closed and open magnetic topologies. A key result is that the overall degree to which the wind is influenced by the field depends largely on a single, dimensionless wind magnetic confinement parameter η* (= BR/v∞), which characterizes the ratio between magnetic field energy density and kinetic energy density of the wind. For weak confinement, η* ≤ 1, the field is fully opened by the wind outflow, but nonetheless, for confinements as small as η* = 1/10 it can have a significant back-influence in enhancing the density and reducing the flow speed near the magnetic equator. For stronger confinement, η* > 1, the magnetic field remains closed over a limited range of latitude and height about the equatorial surface, but eventually is opened into a nearly radial configuration at large radii. Within closed loops, the flow is channeled toward loop tops into shock collisions that are strong enough to produce hard X-rays, with the stagnated material then pulled by gravity back onto the star in quite complex and variable inflow patterns. Within open field flow, the equatorial channeling leads to oblique shocks that are again strong enough to produce X-rays and also lead to a thin, dense, slowly outflowing disk at the magnetic equator. The polar flow is characterized by a faster-than-radial expansion that is more gradual than anticipated in previous one-dimensional flow tube analyses and leads to a much more modest increase in terminal speed (less than 30%), consistent with observational constraints. Overall, the results here provide a dynamical groundwork for interpreting many types of observations—e.g., UV line profile variability, redshifted absorption or emission features, enhanced density-squared emission, and X-ray emission—that might be associated with perturbation of hot-star winds by surface magnetic fields.

Relationship between upstream turbulent boundary-layer velocity fluctuations and separation shock unsteadiness

Abstract: Particle image velocimetry and high-frequency response wall pressure measurements have been used to investigate the relationship between upstream turbulent boundary-layer properties and the unsteady separation shock behavior in a Mach 5 unswept compression ramp interaction No correlation is found between variations in the incoming boundary-layer thickness and the separation shock foot position, as has been suggested in earlier work However, themean velocity proe le, conditioned on theseparation shock foot position, exhibits a subtly fullershape when the shock is downstream than when it is upstream More signie cantly, a clear correlation is observed between positivestreamwisevelocity e uctuations in thelowerthird of the upstream boundary layer and downstream shock motions, and vice versa The strongest correlations are found for velocity e uctuations with frequencies of about4‐10 kHz, which is signie cantly lowerthan the frequencies that characterize the large-scale structures in the boundary layer (40 kHz), although spatial limitations in the transducer array may limit the instrument sensitivity to this lower range These results are qualitatively consistent with the simple physical principle that a fuller velocity proe le imparts increased resistance to separation to the boundary layer and, hence, causes downstream shock motion, whereas a less-full velocity proe le is associated with lower resistance to separation and, hence, upstream shock motion

Large Eddy Simulation of Shock/Boundary-Layer Interaction

Abstract: Reference LIN-ARTICLE-2002-008View record in Web of Science Record created on 2007-05-22, modified on 2016-08-08

Nonstationarity of strong collisionless quasiperpendicular shocks: Theory and full particle numerical simulations

Abstract: Whistler waves are an intrinsic feature of the oblique quasiperpendicular collisionless shock waves. For supercritical shock waves, the ramp region, where an abrupt increase of the magnetic field occurs, can be treated as a nonlinear whistler wave of large amplitude. In addition, oblique shock waves can possess a linear whistler precursor. There exist two critical Mach numbers related to the whistler components of the shock wave, the first is known as a whistler critical Mach number and the second can be referred to as a nonlinear whistler critical Mach number. When the whistler critical Much number is exceeded, a stationary linear wave train cannot stand ahead of the ramp. Above the nonlinear whistler critical Mach number, the stationary nonlinear wave train cannot exist anymore within the shock front. This happens when the nonlinear wave steepening cannot be balanced by the effects of the dispersion and dissipation. In this case nonlinear wave train becomes unstable with respect to overturning. In the present paper it is shown that the nonlinear whistler critical Mach number corresponds to the transition between stationary and nonstationary dynamical behavior of the shock wave. The results of the computer simulations making use of the 1D full particle electromagnetic code demonstrate that the transition to the nonstationarity of the shock front structure is always accompanied by the disappearance of the whistler wave train within the shock front. Using the two-fluid MHD equations, the structure of nonlinear whistler waves in plasmas with finite beta is investigated and the nonlinear whistler critical Mach number is determined. It is suggested a new more general proof of the criteria for small amplitude linear precursor or wake wave trains to exist.

Flare waves observed in Helium I 10 830 Å - A link between Hα Moreton and EIT waves

Abstract: Three traveling disturbances recorded in the absorption line of Helium I at 10830 A (HeI), analogous to HαMoreton waves, are analyzed. The morphology and kinematics of the wavefronts are described in detail. The HeI wave appears as an expanding arc of increased absorption roughly corresponding to the Hα disturbance, although not as sharply defined. HeI perturbations consist of a relatively uniform diffuse component and a patchy one that appears as enhanced absorption in HeI mottles. It leads the Hα front by some 20 Mm and can be followed to considerably larger distances than in Hα observations. Behind the front stationary areas of reduced HeI absorption develop, resembling EUV coronal dimming. The observed HeI as well as the Hα disturbances show a deceleration of the order of 100-1000 ms −2 . Moreover, in the event where Hα ,H eI, and EUV wavefronts are observed, all of them follow closely related kinematical curves, indicating that they are a consequence of a common disturbance. The analysis of spatial perturbation profiles indicates that HeI disturbances consist of a forerunner and a main dip,the latterbeing cospatial withthe Hαdisturbance. The properties and behavior of the wavefronts can be comprehended as a consequence of a fast-mode MHD coronal shock whose front is weakly inclined to the solar surface. The Hα disturbance and the main HeI dip are a consequence of the pressure jump in the corona behind the shock front. The HeI forerunner might be caused by thermal conduction from the oblique shock segments ahead of the shock-chromosphere intersection, or by electron beams accelerated in the quasi-perpendicular section of the shock.

Appearance of Restricted Shock Separation in Rocket Nozzles

Abstract: Uncontrolled flow separation in nozzles of rocket engines is not desired because it can lead to dangerous lateral forces. Different origins for side loads were identified in the past. Meanwhile, it is proven that in thrust-optimized or parabolic nozzles, a major side load occurs as a result of the transition of separation pattern from free shock separation to restricted shock separation and vice versa. Reasons for the transition between the separation patterns are discussed, and the cap-shock pattern, which is identified to be the cause of this transition, is closely analyzed. It turns out that this pattern can be interpreted as an inverse Mach reflection of the internal shock at the nozzle axis. To prove the transition effect as main side-load driver, a subscale test campaign has been performed. Two different nozzle contours, a thrust-optimized and a truncated ideal nozzle with equal performance data, were tested. Highest side loads were measured in the thrust-optimized nozzle, when the separation pattern changes from free to restricted shock separation. Side loads measured in the truncated ideal nozzle were only about one-third as high as in the thrust-optimized nozzle.

Global Shock Waves¶for the Supersonic Flow Past a Perturbed Cone

Abstract: We prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone. The flow is governed by the potential equation, as well as the boundary conditions on the shock and the surface of the body. It is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self-similar solution under some suitable conditions. Our analysis is based on a global uniform weighted energy estimate for the linearized problem. Combining this with the local existence result of Chen–Li [1] we establish the global existence and decay rate of the solution to the nonlinear problem.

Four spacecraft measurements of the quasiperpendicular terrestrial bow shock: Orientation and motion

Abstract: [1] Measurements of the magnetic field at the four Cluster spacecraft, typically separated by ∼600 km, during bow shock crossings allow the orientation and motion of this structure to be estimated. Results from 48 clean and steady quasiperpendicular crossings during 2000 and 2001, covering local times from 0600 to 1700, reveal the bow shock normal to be remarkably stable, under a wide range of steady upstream conditions. Nearly 80% of normals lay within 10° of those of two bow shock models, suggesting that the timing method is accurate to around 10°, and possibly better, and therefore that four spacecraft timings are a useful estimator of the orientation and motion of quasiperpendicular bow shocks. These results show that models provide a good approximation to the bow shock surface and can therefore be used when four spacecraft data are not available. In contrast, only 19% of magnetic coplanarity vectors were within 10° of the model normal. The mean deviation of the coplanarity vector from the timing-derived normal for shocks with θBN < 70° was 22 ± 4°. Typical shock velocities were ∼35 km s−1, although the fastest measured shock was traveling outbound at nearly 150 km s−1.

Particle Image Velocimetry in Mach 3.5 and 4.5 Shock-Tunnel Flows

Abstract: For the e rst time, a particle image velocimetry (PIV) system was used to study high-Mach-number e ows in a shock-tunnel facility with velocities of more than 1.5 km/s and measuring times in the millisecond range. An application of PIV to such a transient high-speed e ow is considerably more dife cult than to a continuous e ow because no online adjustments of the optics and the particle seeding can be done. Additionally, a proper seeding and timingofthefacility iscrucial.Firstwewilldiscussthemeasured velocity e eldbehind acontoured Lavalnozzle (design Mach number4.5 ). The measurement data show that thee owe eld at the nozzleexit is parallel to the nozzle axis and homogeneous as expected from supersonic nozzle theory. The average measured velocity corresponds very well to the calculated e ow velocity. The results are compared to measurements made with a conical Mach 3.5 nozzle that exhibits a diverging e owe eld. A wedge was further introduced into the parallel Mach 4.5 nozzle e ow to study the seed particle performance downstream of an oblique shock. The measured results are also in good agreement with calculated velocities from oblique shock theory. PIV has, therefore, proven to be an efe cient measurement method for high-speed and short-duration simulation facilities.

Control of an Oblique Shock/Boundary-Layer Interaction with Aeroelastic Mesoflaps

Abstract: Aeroelastic mesoe aps for recirculating transpiration have been investigated in an effort to control shock/boundary-layer interactions (SBLIs) through passive cavity recirculation. The mesoe ap concept utilizes a matrix of small e apscovering an enclosed cavity that aredesigned to undergo local aeroelasticdee ection to achieve proper mass bleed or injection when subjected to gasdynamic pressure loading. Experiments were performed to investigate the applicability of the mesoe ap concept for oblique shock interaction by employing shadowgraph e ow visualizations, surface pressure measurements, and mean and e uctuating velocity measurements, along the spanwise midplane of the shock intersection. The experiments were conducted in a Mach 2.41 supersonic wind tunnel operating at a unit Reynolds number of 57 £106 mi1. With the thickest mesoe ap arrays in place, the leading shock formed at the location of the e rst e ap and the boundary-layer thickness at shock impingement was greaterduetoe owinjectionthroughtheupstreame aps.However,thethinnestmesoe aparraysyielded asomewhat reduced boundary-layer thickness downstream of the interaction as a result of the tangential bleeding by the last e aps. Stagnation pressure proe les for the thinnest arrays also showed improved recovery downstream of the SBLI as compared to thesolid-wall case. However, furtherstudy isneeded to investigate three-dimensional effectsand to determine whether this control strategy provides signie cant performance improvements for e ow conditions more consistent with actual inlets.

Stator-Rotor Interactions in a Transonic Compressor—Part 2: Description of a Loss-Producing Mechanism

Abstract: A previously unidentified loss producing mechanism resulting from the interaction of a transonic rotor blade row with an upstream stator blade row is described This additional loss occurs only when the two blade rows are spaced closer together axially Time-accurate simulations of the flow and high-response static pressure measurements acquired on the stator blade surface reveal important aspects of the fluid dynamics of the production of this additional loss At close spacing the rotor bow shock is chopped by the stator trailing edge The chopped bow shock becomes a pressure wave on the upper surface of the stator that is nearly normal to the flow and that propagates upstream In the reference frame relative to this pressure wave, the flow is supersonic and thus a moving shock wave that produces an entropy rise and loss is experienced The effect of this outcome of blade-row interaction is to lower the efficiency, pressure ratio, and mass flow rate observed as blade-row axial spacing is reduced from far to close The magnitude of loss production is affected by the strength of the bow shock and how much it turns as it interacts with the trailing edge of the stator At far spacing the rotor bow shock degenerates into a bow wave before it interacts with the stator trailing edge and no significant pressure wave forms on the stator upper surface For this condition, no additional loss is produced

Formation of reflected electron bursts by the nonstationarity and nonuniformity of a collisionless shock front

Abstract: [1] The impact on electron dynamics of the nonstationarity and nonuniformity of a quasi-perpendicular supercritical collisionless planar shock is analyzed by means of a two-dimensional full-particle electromagnetic simulation code. Trajectories of preselected self-consistent electrons (in contrast with the test particles approach) have been analyzed in order to determine the reflection conditions. Four different classes of reflected electrons have been identified according to the time these spent within the shock front itself before being reinjected into the upstream region. However, the shock front is revealed to be strongly nonstationary and nonuniform (front rippling). Different sources of shock front nonstationarity are shown to take place over different time and spatial scales. The longer time scale is due to the shock front reformation associated to the dynamics of reflected ions. The smaller time scale is due to the propagation of front rippling along the shock front. One key result is that electrons hitting the shock front are not reflected uniformly in time; instead, bursts of energetic reflected electrons are formed by the shock front reformation. In addition, electrons are not reflected uniformly in space, but packs of reflected electrons are formed along the rippled shock front. Comparison of two-dimensional with one-dimensional simulation results evidences that nonuniformity (rippling) of the shock front contributes to diffuse electron bursty patterns both in real and velocities space. Persistent (one-dimensional) and more diffuse (two-dimensional) electron bursts have different impacts on upstream wave emission, which are also discussed.

Numerical study of spherical blast-wave propagation and reflection

Abstract: The objective of this study is to understand the flow structures of weak and strong spherical blast waves either propagating in a free field or interacting with a flat plate. A 5th-order weighted essentially non-oscillatory scheme with a 4th-order Runge-Kutta method is employed to solve the compressible Euler/Navier-Stokes equations in a finite volume approach. The real-gas effects are taken into account when high temperature occurs. A shock-tube problem with the real-gas effect is first tested in order to verify the solver accuracy. Moreover, unsteady shock waves moving over a stationary wedge with various wedge angles, resulting in different types of shock wave reflections, are also tested. It is found that the computed results agreed well with the existing data. Second, the propagation of a weak spherical blast wave, created by rupture of a high-pressure isothermal sphere, in a free field is studied. It is found that there are three minor shock waves moving behind the main shock. Third, the problem of a strong blast wave interacting with a flat plate is investigated. The flow structures associated with single and double Mach reflections are reported in detail. It is found that there are at least three local high-pressure regions near the flat plate.

Electron acceleration and trapping by an oblique shock wave

Abstract: Electron acceleration to ultrarelativistic energies by an oblique magnetosonic shock wave is studied. First, the maximum electron energy is analytically obtained with new simple calculations. The physical mechanism is also discussed in detail. In the wave frame, electrons reflected near the end of the main pulse region, which will be trapped, gain energy from the electric potential and constant electric field Ey0 perpendicular to the external magnetic field. For certain plasma parameters, these electrons can move a long distance in the direction of Ey0 and obtain a great amount of energy from Ey0. It is argued that the trapped electrons can hardly escape from the shock wave. Next, one-dimensional, relativistic, particle simulations are carried out. Theoretical estimates such as the maximum electron energy are found to be in good agreement with the simulations. Simulations also show that the number of trapped electrons continually increases with time.

Observation of supersonic shock wave mitigation by a plasma aero-spike

Abstract: A wind-tunnel model in the shape of a 30° half-angle truncated-cone is designed to generate a strong bow shock behind a weak conical (oblique) shock wave attached to the tip of a protruding central-electrode, in a non-ionized supersonic flow. Plasma is generated between two shocks by an on-board discharge. Its effect on shock waves is explored. The results show that the plasma spike has drastically modified the original complicated shock structure to a simple structure having only a single conical shock attached to the tip of the model, similar to the one generated by a perfect cone.

The interaction of turbulence with shock waves: A basic model

Abstract: The interaction of turbulence and shock waves is considered self-consistently so that the back-reaction of the turbulence and its associated reaction on the turbulence is addressed. This approach differs from previous studies which considered the interaction of linear modes with a shock. The most basic model of hypersonic flow, described by the inviscid form of Burgers’ equation, is used. An energy-containing model which couples the turbulent energy density and correlation length of the flow with the mean flow is developed. Upstream turbulence interacting with a shock wave is found to mediate the shock by (1) increasing the mean shock speed, and (2) decreasing the efficiency of turbulence amplification at the shock as the upstream turbulence energy density is increased. The implication of these results is that the energy in upstream turbulent fluctuations, while being amplified at the shock, is also being converted into mean flow energy downstream. The variance in both the shock speed and position is comp...

Interaction of a Shock Wave with a Cloud of Aluminum Particles in a Channel

Abstract: Interaction of an incident shock wave (with a rectangular or triangular profile behind its front) with a finite-width semi-infinite cloud of aluminum particles located in a channel along the plane of symmetry is numerically simulated. Shock-wave interaction with the leading edge of the cloud results in the formation of a vortex that leads to cloud dispersion. Reflection of the curved shock wave from the plane of symmetry may be regular or may include the formation of the Mach stem. If the cloud is loaded by a rather strong shock wave, a detonation wave is formed in the cloud. In this case, the flow is periodic, which is caused by passing of transverse waves and their reflection from the walls.

Forward-Running Detonation Drivers for High-Enthalpy Shock Tunnels

Abstract: To improve the quality of driving flows generated with detonation-driven shock tunnels operated in the forward-running mode, various detonation drivers with specially designed sections were examined. Four configurations of the specially designed section, three with different converging angles and one with a cavity ring, were simulated by solving the Euler equations implemented with a pseudo kinetic reaction model. From the first three cases, it is observed that the reflection of detonation fronts at the converging wall results in an upstream-traveling shock wave that can increase the flow pressure that has decreased due to expansion waves, which leads to improvement of the driving flow. The configuration with a cavity ring is found to be more promising because the upstream-traveling shock wave appears stronger and the detonation front is less overdriven. Although pressure fluctuations due to shock wave focusing and shock wave reflection are observable in these detonation-drivers, they attenuate very rapidly to an acceptable level as the detonation wave propagates downstream. Based on the numerical observations, a new detonation-driven shock tunnel with a cavity ring is designed and installed for experimental investigation. Experimental results confirm the conclusion drawn from numerical simulations. The generated driving flow in this shock tunnel could maintain uniformity for as long as 4 ms. Feasibility of the proposed detonation driver for high-enthalpy shock tunnels is well demonstrated.

Numerical Simulation of Detonation Initiation with a Shock Wave Entering a Cloud of Aluminum Particles

Abstract: Based on the mathematical model of a reacting two-phase medium in the two-velocity, two-temperature approximation, the process of planar shock wave entering a cloud of aluminum particles is numerically studied. The incident shock wave may have either a rectangular or a triangular profile, i.e., it may be accompanied by a rarefaction wave. An analysis of numerical data allowed us to determine conditions of possible establishment of a steady detonation regime in the cloud. Scenarios of initiation and types of detonation flows in the cloud are determined as functions of the amplitude of the incident shock wave and initiation energy. Criteria of detonation initiation for various fractions of particles are obtained, which express the dependence of the energy stored in the shock wave on its Mach number.

Long time behavior of relativistic ions incessantly accelerated by an oblique shock wave

Abstract: Incessant acceleration of nonthermal fast ions by an oblique magnetosonic shock wave is studied with hybrid simulations. First, magnetic and electric field profiles of an oblique shock wave are obtained by means of a one-dimensional, relativistic, electromagnetic, particle simulation. Test particle trajectories of fast ions are then calculated using these wave profiles. Some fast ions are trapped by the shock wave owing to the relativistic effect that velocity is limited by the speed of light while the momentum can grow indefinitely. In these simulations, some fast ions are found to suffer energy jumps several tens of times; as a result, their final maximum Lorentz factors far exceeded 100.

Effects of wakes on shock-flame interactions and deflagration-to-detonation transition

Abstract: Two-dimensional reactive Navier-Stokes numerical simulations are used to examine the effects of wakesbehind obstacles on shock-flame interactions and deflagration-to-detonation transition in shock-tube experiments. The computations are performed for low-pressure (100 Torr) ethylene/air mixtures using a dynamically adapting computational mesh to resolve flames, shocks, wakes, and vortices in flow. Results of the simulations show that the effect of wakes is similar to the effect of boundary layers studied earlier. The velocity gradient in the wake causes the reflected shock to bifurcate. If the obstacle is large enough, the recirculation area behind the bifurcated shock can entrain the flame, thus accelerating it. The resulting reactive bifurcated structure contains two leading oblique shocks followed by a flame captured by the recirculation flow. This structure grows quickly. Reflections of the oblique bifurcated shocks from side walls careate strong Mach stems that can produce hot sports, new flames, and eventually a detonation. The computational results are consistent with experimental observations of flame acceleration behind reflected shocks.

Normal shock wave-turbulent boundary-layer interactions in the presence of streamwise slots and grooves

Abstract: The effect of streamwise slots and grooves on a normal shock wave-turbulent boundary-layer interaction has been investigated experimentally at a Mach number of 1.3. The surface pressure distribution for the controlled interaction in the presence of slots featured a distinct plateau. This was due to a change in shock structure from a typical unseparated normal shock wave-boundary-layer interaction to a large bifurcated lambda type shock pattern. Velocity measurements downstream of the slots revealed a strong spanwise variation of boundary-layer properties, whereas the modified shock structure was found to be relatively two-dimensional. Cross flow measurements indicate that slots introduce streamwise vortices into the flow. When applied to an aerofoil, streamwise slots have the potential to reduce wave drag while incurring only small viscous penalties. In the presence of grooves the interaction was initially found to be significantly different. A bifurcated shock structure was observed but the trailing leg appeared stronger and featured a second lambda foot. Oil flow visualisation also revealed differences in the interactions, with the region of suction and blowing being limited to a smaller extent of the grooved control surface. The amount of crossflow present was reduced compared to the slotted control surface. By varying the internal geometry of the grooves it was found that the interaction could be modified to be similar to that in the presence of slots indicating that a more practical control device can be designed.

Numerical Study of Wedge Supported Oblique Shock Wave-Oblique Detonation Wave Transitions

Abstract: The results of a numerical study of premixed Hydrogen-air flows ignition by an oblique shock wave (OSW) stabilized by a wedge are presented, in situations when initial and boundary conditions are such that transition between the initial OSW and an oblique detonation wave (ODW) is observed More precisely, the objectives of the paper are: (i) to identify the different possible structures of the transition region that exist between the initial OSW and the resulting ODW and (ii) to evidence the effect on the ODW of an abrupt decrease of the wedge angle in such a way that the final part of the wedge surface becomes parallel to the initial flow For such a geometrical configuration and for the initial and boundary conditions considered, the overdriven detonation supported by the initial wedge angle is found to relax towards a Chapman-Jouguet detonation in the region where the wedge surface is parallel to the initial flow Computations are performed using an adaptive, unstructured grid, finite volume computer code previously developed for the sake of the computations of high speed, compressible flows of reactive gas mixtures Physico-chemical properties are functions of the local mixture composition, temperature and pressure, and they are computed using the CHEMKIN-II subroutines

Influence of Endwall Contouring on the Transonic Flow in a Compressor Blade

Abstract: Endwall contouring is successfully applied to compressor rotors to reduce boundary layer loading and to control endwall flow. Over-speeds resulting from large relative thickness and curvature of the rotor root section are compensated by the increase in open flow area which is generated by the concave hub shape. In transonic flow this area increase promotes higher Mach numbers and has a considerable impact on the shock system. To investigate endwall contouring experimentally at engine like flow conditions a novel cascade technique is introduced: A contracting endwall is designed in a way to enable homogenious flow conditions in Mach number and flow angle at the inlet plane of the cascade. For a given blade shape now several endwall contours may be investigated. Experiments are performed at the High Speed Cascade Windtunnel of the University of the Armed Forces, Munich for a linear and a concave endwall for a given blade section. Inlet Mach number level is around Ma1 = 0.9 at typical turning and profile thickness. The results show an increase in pre-shock Mach number and a change in shock pattern from an oblique shock for the linear contour to a normal shock for the concave one. Endwall contouring is demonstrated not only to influence the flow in the vicinity of the endwall but to extend up to a considerable distance in spanwise direction.Copyright © 2002 by ASME

Calculation of Dust Lifting by a Transient Shock Wave

Abstract: A mathematical model of lifting of dust particles under the action of transient shock waves is proposed, which takes into account a simultaneous action of the Saffman force and aerodynamic interference on the particle. This model provides an adequate description of the initial stage of lifting of single particles of a dusty layer under the action of shock waves of weak and moderate strength. Satisfactory agreement of numerical and experimental data is reached. It is shown that particle lifting is caused by the action of the Saffman force in the case of weak shock waves (the shock-wave Mach number is less than 1.5) and medium-sized particles (the particle diameter is less than 100 μm) and aerodynamic interference between the particle and the surface in the case of shock waves of moderate strength (the shock-wave Mach number is 2.1–3.3) and large particles (the particle diameter is 200–250 μm). Key words: two-phase flows, shock waves, formation of gas mixtures.

Evolution of Upstream Propagating Shock Waves From a Transonic Compressor Rotor

Abstract: The evolution of upstream propagating shock waves from the isolated transonic compressor designated NASA Rotor-35 is examined numerically. Results from the numerical simulations are compared with those from a semi-analytical two-dimensional model based on the nonlinear acoustic interaction of shock waves in the axial–tangential plane upstream of the rotor. The evolution determined from a two-dimensional viscous computational solution is found to agree well with the semi-analytical prediction and confirms that shock wave evolution is a primarily inviscid phenomenon. Radial variations are found to increase the rate of decay of the shock wave amplitude in comparison to the prediction from the semi-analytical two-dimensional model. The velocity field from the three-dimensional viscous solution compares well with experimental measurements, indicating that the initial shock strength and shock wave evolution immediately upstream of the rotor blade leading edge are accurately captured. The upstream-propagating shock system is found responsible for nearly 20% of the total loss attributable to the rotor, and is consistent with earlier transonic airfoil cascade studies. The axial decay rate of the upstream induced circumferential static pressure distortion is found to be an order of magnitude slower at spanwise locations with supersonic relative inlet Mach numbers than those at which it is subsonic. As a consequence of this slower decay rate, it is found that the axial gap to the upstream stator would need to be about twice that used for subsonic blade sections.© 2002 ASME

A numerical investigation of broad-band shock noise

Abstract: The interaction between a spatially developing, turbulent shear layer (Mc — 0.6) and an isolated oblique compression wave (AP/P^ = 0.2) is studied by direct numerical simulation. Analysis is performed on three key elements of this problem, namely the oblique compression-expansion wave, the associated acoustic field and the shear-layer turbulence. The acoustic field consists of two separate components: the downstream propagating mixing noise originating from the transitional region of the shear layer, and a nearly omni-directional shock noise component from a region slightly downstream of the interaction location. The shock noise component dominates the upstream radiation but its relative importance diminishes in the downstream direction. The frequency spectrum of the shock noise has a peak centered around fS^/AU = 1.17, which is slightly higher than that of mixing noise. In the near field, self-similar turbulence is shown to be established before the interaction. Two-point correlation of the turbulent fluctuations confirms the importance of accounting for the spatial coherence of the turbulence in any shock noise model. Minimal oscillations of the compression wave are observed. This is in sharp contrast to the two-dimensional shock-vortex study by Manning & Lele [8] in which substantial shock motion was observed.