Showing papers on "Supersonic speed published in 2000"

Subgrid-Scale Models for Large-Eddy Simulations of Compressible Wall Bounded Flows

Abstract: A comparative assessment of six subgrid-scale models is presented in the case of a compressible plane channel flow over isothermal walls, four of which are based on the recent mixed-scale model. A supersonic and a subsonic case in temporal development at Mach 1.5 and 0.5, respectively, are considered for a Reynolds number equal to 3000, with comparison to the direct numerical simulations (DNS) of Coleman et al. in the first case, and the incompressible DNS of Kim et al. in the second case. For each Mach number, two grids are considered, with about 20 and 5 times less grid points as in the reference DNS, and the results are globally satisfactory, although not excellent. In particular, the wall friction is globally underestimated by about 10%, both in the subsonic and the supersonic cases. Among the models tested are several original combinations, which vanish at the wall without requiring any damping function

Multiobjective evolutionary computation for supersonic wing-shape optimization

Abstract: This paper discusses the design optimization of a wing for supersonic transport (SST) using a multiple-objective genetic algorithm (MOGA). Three objective functions are used to minimize the drag for supersonic cruise, the drag for transonic cruise, and the bending moment at the wing root for supersonic cruise. The wing shape is defined by 66 design variables. A Euler flow code is used to evaluate supersonic performance, and a potential flow code is used to evaluate transonic performance. To reduce the total computational time, flow calculations are parallelized on an NEC SX-4 computer using 32 processing elements. The detailed analysis of the resulting Pareto front suggests a renewed interest in the arrow wing planform for the supersonic wing.

A proof of existence of perturbed steady transonic shocks via a free boundary problem

Abstract: We prove the existence of a solution of a free boundary problem for the transonic small-disturbance equation The free boundary is the position of a transonic shock dividing two regions of smooth flow Assuming inviscid, irrotational flow, as modeled by the transonic small-disturbance equation, the equation is hyperbolic upstream where the flow is supersonic, and elliptic in the downstream subsonic region To study the stability of a uniform planar transonic shock, we consider perturbation by a steady C1+ϵ upstream disturbance If the upstream disturbance is small in a C1 sense, then there is a steady solution in which the downstream flow and the transonic shock are Holder-continuous perturbations of the uniform configuration This result provides a new use of inviscid perturbation techniques to demonstrate, in two dimensions, the stability of transonic shock waves of the type that appear, for example, over the wing of an airplane, along an airfoil, or as bow shocks in a flow with a supersonic free-stream velocity © 2000 John Wiley & Sons, Inc

Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number

Abstract: Large eddy simulation (LES) of compressible periodic channel flow is performed using a fourth-order finite difference scheme for a Reynolds number based on bulk density, bulk velocity and channel half-width equal to 3000. Two configurations are studied: a subsonic case (M0=0.5) that corresponds to the experiments of Niederschulte et al. [‘Measurements of turbulent flow in a channel at low Reynolds numbers’, Exp. Fluids, 9, 222–230 (1990)] and a supersonic case (M0=1.5) that corresponds to the direct numerical simulation (DNS) results by Coleman et al. [‘A numerical study of turbulent supersonic isothermal-wall channel flow’, J. Fluid Mech., 305, 159–183 (1995); ‘Compressible turbulent channel flows: DNS results and modeling’, J. Fluid Mech., 305, 185–218 (1995)]. In order to determine the influence of the discretization, two cases are computed using two different meshes, a coarse one and a fine one. Two subgrid-scale models are tested: the first one is an extension to compressible flows of the Smagorinsky model, while the second one is a model based both on large and small scales of turbulence, a hybrid Bardina–selective mixed scale model. Various statistical comparisons are made with experimental and DNS data at similar Reynolds numbers, including higher-order statistics. Copyright © 2000 John Wiley & Sons, Ltd.

Laser-excited Mach cones in a dusty plasma crystal

Abstract: Experimental studies of the formation and structure of Mach cones in a plasma crystal are presented. Plasma crystals are ordered structures of charged microspheres trapped in the sheath of an rf discharge plasma. Using a monolayer crystal with a hexagonal lattice, Mach cones were excited by the radiation pressure of a focused laser beam. The beam was swept at a supersonic speed through the crystal, in a controlled and repeatable manner. A multiple Mach cone structure was observed, with at least three distinct Mach cones. The Mach angle relation was verified over a wide range of Mach numbers, for both the first and second cones. The sound speed, measured from the first Mach angle, was found to increase with the particle number density. Two methods of determining the particle charge and screening distance are developed, making use of the sound speed and an assumption of a Yukawa interparticle potential. Molecular-dynamics simulations of the experiment were carried out, using a monolayer of particles interacting through a Yukawa potential, and these show close agreement with the experiment.

Mach cone shocks in a two-dimensional Yukawa solid using a complex plasma

Abstract: Mach cones were studied experimentally in a two-dimensional Yukawa solid consisting of charged micrometer particles suspended as a layer in a plasma. These cones were V-shaped shocks produced spontaneously by a supersonic particle moving below the main two-dimensional particle layer. The cones had a double structure. The first cone was compressional and particles moved forward, and it was followed by a second cone, which was rarefactional, where particles moved backward. Over the limited range of speed V attained by the supersonic particles in this experiment, the angle $\ensuremath{\mu}$ of the cone was found to obey the Mach cone rule $\mathrm{sin}\ensuremath{\mu}=c/V,$ where c is the medium's sound speed. The cones caused only elastic deformations in the crystal lattice, except in a narrow track behind the cone's vertex. The wings of the cones can be analyzed as linear shocks in two dimensions. Using spatially resolved measurements of the particle number density and velocity and applying the Hugoniot relations for shocks in two dimensions, we found that the pressure inside the first Mach cone was greater than in the undisturbed medium by a factor of $1.3--1.6.$ The cone angle was also used to measure the charge in this experiment.

Numerical Investigation of Hydrogen Strut Injections into Supersonic Airflows

Abstract: The ine uence of different injector geometries on the mixing behavior of planar supersonic jets is investigated. Hydrogenisinjectedinthee owdirectionthroughthebluntendofastrut.Differentlipthicknessesattheinjectorend induce different extents of recirculation zones. Additionally, changes are caused within the shock-wave/expansion fan pattern at the injector exit that have an important ine uence on loss in total pressure. The accuracy of the used numerical scheme is demonstrated for one injector geometry by comparison with experimental data. Based on this cone guration, modie cations in lip thickness and injection Mach number are investigated numerically and are assessed using several calculated performance parameters. Results show that the chosen lip thickness has a much stronger ine uence on loss in total pressure than moderate modie cations in injector length and height. For the very thin hydrogen jets that were investigated, the mixing efe ciency is nearly independent on injector lip thickness.

Experimental investigation of mixing and ignition of transverse jets in supersonic crossflows

Abstract: Ignition, flame-holding, and mixing enhancement are fundamental aspects of supersonic combustion and are critical to the development of hypersonic airbreathing propulsion engines. High velocities associated with supersonic/hypersonic flight speeds constrain the performance of propulsion systems because of the limited flow residence time inside the combustor. A useful hypervelocity propulsion system therefore requires enhanced mixing of fuel and air, injection with very low drag penalty, and effective distribution of fuel over the burner cross-section. One of the simplest approaches is the transverse injection of fuel from wall orifices. The interesting but rather complicated flow-field dynamics of transverse jets injected into a supersonic crossflow has been studied by many supersonic combustion researchers since 1960’s, but with limited freestream flow conditions. Most of the previous research was performed in conventional wind tunnels by accelerating cold air into supersonic conditions, namely in low velocity and low total enthalpy flow conditions. However, a real supersonic combustor environment at flight speeds beyond Mach 8 can only be simulated using impulse facilities due to the required high total enthalpies. Among various impulse facilities, expansion tubes are especially useful in providing high total enthalpy flows with the proper chemical composition, namely the absence of dissociated species. This research is focused on studying the near-field mixing and ignition properties of transverse fuel jets injected into realistic supersonic combustor flows. We use advanced flow visualization techniques, namely planar laser-induced fluorescence (PLIF) imaging of the hydroxyl radical (OH) and ultra-fast-framing-rate schlieren imaging. While schlieren indicates the location of shock waves, jet penetration and large scale flow features, OH-PLIF is used to map the regions of ignition. The first objective of the present work is to characterize the expansion tube facility

Crackle - A dominant component of supersonic jet mixing noise 13; 13;

Abstract: This paper examines the generation of a particular noise, referred to as crackle, first observed by Ffowcs Williams et al. in a full-scale jet engine. Schlieren pictures along with far-field acoustic data obtained for high-temperature axisymmetric supersonic jets were used to examine the crackle characteristics. Experimental data from a full-scale engine were also used to validate the features obtained from small-scale laboratory experiments. The experimental data cover a velocity range from 600 m/s to 1.05 km/s. A schlieren picture of the radiation field of an M = 2 high temperature jet (U(j) = 1.05 km/s), depicts shock-wavelike structures emanating from the jet and propagating in the downstream direction at shallow angles to the jet axis. The frequency of occurrence of these intense waves increases with jet exit velocity/temperature. It is suggested that microexplosions of the cold entrained ambient fluid in the hot jet generate these intense waves, which are believed to be associated with crackle. When an entrained cold lump of fluid is exposed suddenly to the hot jet fiuid, it expands, giving rise to a monopole source of sound. The convection of the monopoles at supersonic speed leads to the observed directionality of the wave front/crackle sound. (Author)

Diffusive, supersonic x-ray transport in radiatively heated foam cylinders

Abstract: Diffusive supersonic radiation transport, where the ratio of the diffusive radiation front velocity to the material sound speed >2 has been studied in experiments on low density (40 mg/cc to 50 mg/cc) foams. Laser-heated Au hohlraums provided a radiation drive that heated SiO2 and Ta2O5 aerogel foams of varying lengths. Face-on emission measurements at 550 eV provided clean signatures of the radiation breakout. The high quality data provides new detailed information on the importance of both the fill and wall material opacities and heat capacities in determining the radiation front speed and curvature. The Marshak radiation wave transport is studied in a geometry that allows direct comparisons with analytic models and two-dimensional code simulations. Experiments show important effects that will affect even nondiffusive and transonic radiation transport experiments studied by others in the field. This work is of basic science interest with applications to inertial confinement fusion and astrophysics.

Self-consistent hybrid simulations of the interaction of the heliosphere with the local interstellar medium

Abstract: A new method for investigating the interaction of the solar wind with the partially ionized local interstellar medium (LISM) is presented. The solar wind and the interstellar plasma are modeled using a two-dimensional (2-D) hydrodynamic numerical code. The plasma is coupled to the neutral hydrogen (of both interstellar and solar wind origin) via resonant charge exchange. To model the neutral H distribution, we use a nonstationary 2.5-D particle mesh, method to solve the Boltzmann equation, which is coupled self-consistently to the interstellar and solar wind plasma. Numerical self-consistency is achieved by iterating the plasma and neutral H distributions between the two numerical schemes until a steady state is achieved. Results from three test applications are presented and discussed, including the first one-shock kinetic simulation. The simulations are able to reproduce the main features of the heliosphere such as shock structure, hydrogen wall, and heating, deceleration and filtration of neutral hydrogen. In addition, they enable the study and interpretation of the non-Maxwellian hydrogen distribution function. Traces of fast neutrals originating inside the termination shock and the heliosheath/heliotail region can be found far upstream of the outer heliosphere. The influence of different interstellar plasma boundary values on the heliosphere is highlighted in the comparison of two supersonic simulations and one subsonic simulation. In particular, by comparing the simulated energetic neutral atom (ENA) fluxes at 1 AU of the supersonic and subsonic models, it is found that the subsonic flux is significantly underabundant in the energy range 10 – 60 eV compared to the supersonic case. This may offer an important diagnostic for determining whether the heliosphere possesses a bow shock or not.

On the Stability of Colliding Flows: Radiative Shocks, ThinShells, and Supersonic Turbulence

Abstract: High-resolution numerical simulations reveal the turbulent character of the interaction zone of colliding, radiative, hypersonic flows As the shocked gas cools radiatively, the cooled matter is squeezed into thin, high density shells The remaining kinetic energy causes supersonic turbulence within these shells, before it is finally dissipated by internal shocks and vortex cascades The density is far from homogeneous High density filaments and large voids coexist Its mean value is significantly below the stationary value Similarly, areas with supersonic velocities are found next to subsonic regions The mean velocity is slightly below or above the sound speed While quasi uniform flow motions are observed on smaller scales the large scale velocity distribution is isotropic Part of the turbulent shell is occupied by relatively uniform flow-patches, resembling coherent structures Astronomical implications of the turbulent interaction zone are multifarious It probably drives the X-ray variability in colliding wind binaries as well as the surprising dust formation on orbital scales in some WR-binaries It lets us understand the knotty appearance of wind-driven structures as planetary and WR-ring nebulae, symbiotics, supernova remnants, galactic supperbubbles Also, WR and other radiatively driven, clumpy winds, advection dominated accretion, cooling flows and molecular cloud dynamics in star-forming regions may carry its stamp

A Method for Calculating Transient Surface Temperatures and Surface Heating Rates for High-Speed Aircraft

Abstract: This report describes a method that can calculate transient aerodynamic heating and transient surface temperatures at supersonic and hypersonic speeds. This method can rapidly calculate temperature and heating rate time-histories for complete flight trajectories. Semi-empirical theories are used to calculate laminar and turbulent heat transfer coefficients and a procedure for estimating boundary-layer transition is included. Results from this method are compared with flight data from the X-15 research vehicle, YF-12 airplane, and the Space Shuttle Orbiter. These comparisons show that the calculated values are in good agreement with the measured flight data.

The Galactic Shock Pump: A Source of Supersonic Internal Motions in the Cool Interstellar Medium

Abstract: We propose that galactic shocks propagating through interstellar density fluctuations provide a mechanism for the intermittent replenishment, or "pumping," of the supersonic motions and internal density enhancements observed pervasively within cool atomic and molecular interstellar structures, without necessarily requiring the presence of self-gravity, magnetic fields, or young stars. The shocks are assumed to be due to a variety of galactic sources on a range of scales. An analytic result for the kinematic vorticity generated by a shock passing through a radially stratified two-dimensional isobaric model cloud is derived, assuming that the Mach number is not so large that the cloud is disrupted, and neglecting the shock curvature and cloud distortion. Two-dimensional lattice gas hydrodynamic simulations at modest Mach numbers were used to verify the analytic result. The induced internal velocities are initially a significant fraction of the shock speed divided by the square root of the density contrast, accounting for both the observed line width amplitudes and the apparent cloud-to-cloud line width-density scaling. The line width-size relation could then be interpreted in terms of the well-known power spectrum of a system of shocks. The induced vortical energy should quickly be converted to compressible and MHD modes and so would be difficult to observe directly, even though it would still be the power source for the other modes. The shock pump thus produces density structure without the necessity of any sort of instability. We argue that the shock pump should lead to nested shock-induced structures, providing a cascade mechanism for supersonic "turbulence" and a physical explanation for the fractal-like structure of the cool interstellar medium. The average time between shock exposures for an idealized cloud in our Galaxy is estimated and found to be small enough that the shock pump is capable of sustaining the supersonic motions against readjustment and dissipation, except for the smallest structures. This suggests an explanation of the roughly spatially uniform and nearly sonic line widths in small "dense cores." We speculate that the avoidance of shock pumping may be necessary for a localized region to form stars and that the inverse dependence of probability of avoidance on region size may be an important factor in determining the stellar initial mass function.

Detailed measurements of a diffusive supersonic wave in a radiatively heated foam

Abstract: We have made the first detailed measurements of a diffusive supersonic radiation wave in the laboratory. A 10 mg/cm(3) SiO2 foam is radiatively heated by the x-ray flux from a laser-irradiated hohlraum. The resulting radiation wave propagates axially through the optically thick foam and is measured via time-resolved x-ray imaging as it breaks out the far end. The data show that the radiation wave breaks out at the center prior to breaking out at the edges, indicating a significant curvature in the radiation front. This curvature is primarily due to energy loss into the walls surrounding the foam.

Two-dimensional wake potentials in sub- and supersonic dusty plasmas

Abstract: Hot electrons and sub- and supersonic flows of cold ions around a charged dust particle create steady state wake and Debye screening fields. These linear, electrostatic fields are studied in two-dimensional planar or cylindrical geometry. An asymptotic analysis in the limit of large (compared to Debye length) downstream coordinate z yields analytic wakefields that are in good agreement with numerical integrations of the linear, steady state response function.

Pitot pressures of correctly-expanded and underexpanded free jets from axisymmetric supersonic nozzles

Abstract: The structures of the axisymmetric free jets from supersonic nozzles with the exit Mach numbers of 1.5 and 2.0 are studied with special attention to the decay of the Pitot pressures downstream of the Mach disk. The Pitot pressure probe and schlieren method are used in the experiments to diagnose the flowfield. A TVD numerical method is also applied to the Euler equations, and the computed jet structures are compared with experiments. In the underexpanded jet, the experimentally obtained Pitot pressure near the jet centerline is found to substantially recover downstream of the Mach disk. By comparing the numerical computation, this phenomenon is thought to be caused by the turbulent momentum transfer to the central region from the region outside the slip line where the stagnation pressure loss is small.

Radial discontinuities in tokamak magnetohydrodynamic equilibria with poloidal flow

Abstract: It is shown that transonic poloidal flow leads to ideal magnetohydrodynamic tokamak equilibria with radial discontinuities in the density, pressure, and flow velocity profiles. Transonic profiles are defined as having flow velocities ranging from subsonic to supersonic with respect to the poloidal sound speed (csBp/B). The jump of the equilibrium quantities occurs approximately at the sonic surface and its magnitude is of order e1/2 (e is the inverse aspect ratio). Because of the large velocity shear at the sonic surface, transonic profiles may improve energy confinement as suggested by current understanding of tokamak plasma turbulence suppression.

Numerical Simulation of a Three-Dimensional Flame/Shock Wave Interaction

Abstract: A three-dimensional Navier-Stokes solver for chemically reacting flows is used to study the structure of a supersonic hydrogen-air flame stabilized in a Mach 2.4 rectangular cross-section wind tunnel. The numerical model uses a 9-species, 21-reaction hydrogen oxidation mechanism and employs Menter's hybrid κ-ω/κ-e turbulence model. An assumed probability density function is used to account for the effects of turbulent temperature fluctuations on the ensemble-averaged chemical reaction rates. Results are presented for a configuration studied at the University of Michigan in which the effects of wedge-generated shock waves on flame stability were determined. Computed pitot and static pressure profiles are compared with experimental measurements, and axial density gradient contour plots are compared with experimental schlieren photographs. The highly three-dimensional structure of the flame is described in detail, and stabilization mechanisms are discussed

Effects of high-speed tunnel noise on laminar-turbulent transition

Abstract: It is well known that the high levels of noise present in conventional hypersonic ground-test facilities cause transition to occur earlier than in e ight. Flight measurements of incoming noise are reviewed and compared with measurements in ground-test facilities, of both conventional and quiet design, at hypersonic and high supersonic speeds. The low noise present in e ight is apparently the reason for the very large transition Reynolds numbers sometimes measured in e ight, when roughness, crosse ow, and other factors are controlled. Design will usually involve consideration of the trend in transition when a parameter is varied. The effect of facility noise on these trends is reviewed. In some cases, the trend of conventional-tunnel data is opposite to the trend in quiet-tunnel data. Thus, transition measurements in conventional ground-test facilities are not reliable predictors of e ight performance, except perhaps in special cases.

Supersonic external-compression diffuser and method for designing same

Abstract: A supersonic external-compression inlet (20) comprises a generally scoop-shaped supersonic compression section for diffusing a supersonic free stream flow (24). The supersonic compression section includes a main wall having a leading edge (28) and a throat portion downstream of the leading edge (28), and side portions joined to opposite side edges of the main wall so as to form a generally scoop-shaped structure. The side portions advantageously extend into the supersonic flow stream far enough to encompass the initial oblique shock wave that is attached to the leading edge of the main wall. The main wall has an inner surface (22) formed generally as an angular sector of a surface of revolution, the inner surface (22) of the main wall coacting with inner surfaces of the side portions to define a three-dimensional external-compression surface. The supersonic external-compression inlet (20) also includes a subsonic diffuser section arranged to receive flow from the supersonic compression section and to diffuse the flow to a subsonic condition. A variable-geometry inlet includes an external ramp hinged about its forward edge and forming a portion of the inner surface of the scoop-shaped diffuser, pivotal movement of the external ramp serving to vary a throat size of the inlet. The subsonic diffuser (20) includes an internal ramp hinged about its aft edge for maintaining a smooth transition from the external ramp.

Laser-Generated Localized Freestream Perturbations in Supersonic and Hypersonic Flows

Abstract: An optical method for generating localized, controlled perturbations has been developed for use in supersonic and hypersonic flowfields The thermal spot disturbance is generated when the pulsed beam from a laser is focused at the desired origin and a small region of the gas is ionized After recombination, the thermal spot persists as a region of heated gas that convects with the local flow velocity The perturbation is approximately spherical and several millimeters in diameter, with the size dependent on the flow density Optimal formation of the perturbation is achieved with large-F-number focusing systems To date, the disturbance has been used as a freestream perturbation for supersonic receptivity experiments as well as forward-facing cavity and blunt-body shock oscillation studies

Comparison of Supersonic Combustion Between Impulse and Vitiation-Heated Facilities

Abstract: A comparison has been made between supersonic combustion in two commonly used, but fundamentally different, facilities for scramjet research, a vitiation-heated blowdown tunnel and a free-piston shock tunnel. By passing the shock-tunnel freestream flow through a normal shock and then expanding it to Mach 2.5, combustor inlet conditions and geometries were nominally replicated between the two facilities. A constant-area rectangular duct and a diverging duct, both employing central-strut hydrogen injection, were used. Boundary-layer separation and choking in the constant-area duct limited supersonic combustion comparisons up to a fuel equivalence ratio of the order of 0.3. The experimental results also show that the onset of boundary-layer separation occurs at the same combustor pressure loads and that it behaves similarly in the different facilities. With the diverging duct, comparisons were made up to an equivalence ratio of 1.05. Agreement between the results obtained in the two facilities is within experimental error when the different freestream and boundary layers are accounted for.

Eddy Convection in Coaxial Supersonic Jets

Abstract: Wepresent experimentalresultson themorphology and evolution of large turbulenteddiesin coaxial supersonic jets.ThestudyencompassedMach1.5,axisymmetric,perfectlyexpandedjetscomposedofairoramixtureofhelium and air. A double-exposure planar laser-induced e uorescence (PLIF) system, with gaseous acetone as the tracer molecule, enabled visualization of the turbulent structure and of its evolution a short time later. The convective velocityoftheeddieswasextractedfromthePLIFimagesbymeansoftwo-dimensionalcrosscorrelations.Eddiesin theair jet propagatewith a speed approximately 80% ofthelocal centerline mean velocity. In thefaster helium-air jets eddies aremeasured to be supersonic with respect to the ambient air, a result corroborated by thevisualization of Mach waves. In the helium-air jet addition of a Mach 0.82 secondary e ow reduces the convective velocity of the primary eddies from 70 to 62% of the primary exit velocity. The speed of the secondary eddies is 44% of the secondary exit velocity. All turbulent motions in this coaxial helium-air jet are intrinsically subsonic, leading to substantial reduction of Mach waves and reduction in noise. A ree ned empirical model for eddy convection in compressible jets is proposed. The results of this study are relevant to mixing, combustion, and jet noise.

Numerical Simulation of Transient Jet-Interaction Phenomenology in a Supersonic Freestream

Abstract: The objective is to evaluate the transient effects of a reaction control jet on the aerodynamic performance of a genericinterceptormissileoperating at supersonice ightconditions.Three-dimensionalcomputationsofthehighly turbulent e owe eld produced by a pulsed, supersonic, lateral-jet control thruster interacting with the supersonic freestream and missile boundary layer of a generic interceptor missile are evaluated at different altitudes and thruster conditions. A generic missile interceptor cone guration consisting of a long, slender body containing e xed dorsal and tail e ns is simulated. Parametric computational e uid dynamic solutions are obtained at altitude conditions corresponding to 19.7 and 35.1 km for 1 ) steady-state conditions with the lateral control jet turned off, 2) steady-state conditions with the lateral control jet turned on, 3 ) transient jet startup conditions, and 4 ) transient jet shutdown conditions. A thermally and calorically perfect gas with a specie c heat ratio equal to 1.4 was assumed for both the Mach number 5 freestream and Mach number 3 lateral jet. Vehicle forces and moments are assessed from each solution by integrating the surface pressures and viscous shear stresses computed on the missile surfaces. These results are used to determine the ine uence of the jet-interaction effects on the transient aerodynamicperformanceofthemissile.Theanalysispredictsstrongtransientine uencesfortheintegratednormal force and pitching moment.