Cone Boundary Research Articles

Effect of wall microstructure on conical hypersonic boundary layer flow

As an effective boundary layer flow control method, wall microstructure has an important application prospect in heat and drag reduction of hypersonic. In this paper, based on experimental techniques such as high-frequency pressure fluctuation testing, the effects of different microstructure configurations (V-shaped and rectangular) and distribution modes (streamwise and transverse) on the flow of hypersonic conic boundary layer under the condition of Mach 6 hypersonic incoming flow are studied. The experimental results show that compared with the flow of the smooth wall boundary layer, the wall microstructure has a greater influence on the eigenfrequency of the second-mode wave in the boundary layer, and the streamwise increases by about 20 kHz to the rectangular microstructure and decreases by about 30 kHz to the transverse rectangular microstructure. At the same time, the transverse V-shaped microstructure can increase the amplitude of the second mode in the boundary layer by 5.5 times compared with the smooth wall. For the evolution of boundary layer flow, the microstructure arranged along the flow direction will accelerate the linear development of the disturbance wave during the transition, so that the laminar flow will be transformed into turbulent flow in a shorter distance. The microstructure arranged along the transverse direction prolongs the linear development stage of the disturbance wave during the transition, so that the laminar flow turns into turbulent flow over a longer distance. Downstream of different structures, it is shown that transverse rectangular microstructure has lowest temperatures.

Controllable cone for horizontal landing on asteroids using a flexible probe

The recently proposed flexible probe for asteroids provides a novel scheme for landing on low-gravity surface. To understand the feasible initial condition of the flexible probe's horizontal landing trajectory under multiple constraints, a controllable cone is defined and investigated. The boundary of the controllable cone is calculated using a double-layer optimization method. In the inner-layer, the switching time of the thrust profile is fixed, and the boundary point is solved through a multi-constraint trajectory optimization problem that considers the influence caused by the flexible deformation. In the outer-layer, the switching time of the thrust profile is optimized to maximize the cone boundary. To improve the optimization efficiency, an adaptive interval is used to search the switching time. With the double-layer optimization method, the controllable cone boundaries can be generated for both a specific height and a three-dimensional space. The controllable cone of the flexible probe is simulated for the landing on asteroid 433 Eros, and the influence of the flexible deformation is also analyzed.

Effect of wall-seeping gas film under different working media on stability of conical hypersonic boundary layer

Wall-seeping gas film (WSGF) is a promising method of controlling hypersonic boundary layer transition and reducing friction drag and heat transfer. Experiments are conducted in a Mach 6 hypersonic quiet wind tunnel by using nano-tracer planar laser scattering (NPLS) and high-frequency fluctuating pressure measuring technique. This work investigates the effects of wall-seeping helium, air, and carbon dioxide gas films under identical volume flow rate condition on conical boundary layer thickness, disturbance wave structure, wavelength, frequency, amplitude, and nonlinear interaction. The experimental results reveal that the WSGF significantly thickens the hypersonic boundary layer, with the thickest position appearing at the downstream boundary of the seeping zone. The boundary layer thickness is thinnest for helium gas film but thickest for carbon dioxide gas film. Generally, air gas film and carbon dioxide gas film induce the regular, rope-like, and interlaced second-mode waves to appear in advance in the boundary layer. However, under a higher volume flow rate for carbon dioxide gas film, the disturbance wave structure resembles interface fluctuations, with a characteristic wavelength of approximately 18 mm and a peak frequency as low as about 35 kHz, but no the rope-like interlaced characteristic. At this time, the influence of shear layer instability becomes significant. The disturbance waves do not exhibit second-mode wave characteristics for wall-seeping helium gas film, whose shape is irregular and undergoes deformation with time and space. Additionally, the power spectral density of wall fluctuating pressure exhibits insignificant variation with volume flow rate and flow direction, which is similar to the characteristic of power spectral density in the laminar boundary layer and has no peak frequency. The wavelength of second-mode waves is about 2－3 times the boundary layer thickness for air gas film, and increases to more than 3 times for carbon dioxide gas film. The application of carbon dioxide gas film results in smaller peak frequency and bandwidth of disturbance wave, larger characteristic wavelength and amplitude, longer propagation distance, and stronger nonlinear interaction than the application of air gas film. In the future, attention should be paid to understanding disturbance wave characteristics in the boundary layer for the helium gas film and shear layer instability under larger volume flow rates.

Geometric Properties of Blaschke-Like Maps on Domains with a Conic Boundary

Geometric Properties of Blaschke-Like Maps on Domains with a Conic Boundary

Effect of local wall temperature on hypersonic boundary layer stability and transition

Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is complicated when the wall temperature distribution is nonuniform, and researchers have experimentally found that local wall cooling may delay the onset of transition. We attempt to clarify the physical mechanisms whereby the local wall temperature affects the transition and the stability of a hypersonic boundary layer. A numerical investigation of the disturbance evolution in a Mach-6 sharp cone boundary layer with local wall heating or cooling is conducted. Direct numerical simulation (DNS) is performed for the single-frequency and broadband disturbance evolution caused by random forcing. We vary the local wall temperature and the location of heating/cooling, and then use the e N method to estimate the transition onset. Our results show that local wall cooling amplifies high-frequency unstable waves while stabilizing low-frequency unstable waves, with local heating amplifying all unstable waves locally. The disturbance amplitude and second-mode peak frequency obtained by DNS agree well with the previous experimental results. Local cooling/heating has a dual effect on the stability of the hypersonic boundary layer. For local cooling, while it effectively inhibits the growth of the low-frequency unstable waves that dominate the transition downstream, it also further destabilizes the downstream flow. In addition, while upstream cooling can delay the transition, excessive cooling may promote it; local heating always slightly promotes the transition. Finally, recommendations are given for practical engineering applications based on the present results.

Effects of entropy layer on the boundary layer over hypersonic blunt cones considering chemical reactions

In this study, the effects of entropy layer on the boundary layer over hypersonic blunt cones for a thermochemical equilibrium gas are investigated. The flow and stability characteristics of the entropy and boundary layers are presented considering the chemical reactions. It is found that the entropy layer has little influence on the inner layer inside the boundary layer. The inner layer thickness increases when chemical equilibrium is considered, which stems from the enhanced viscosity protection near the wall surface. At the leading edge of the blunt cone, due to the effects of the equilibrium gas, the temperature in the boundary and entropy layers decreases and the boundary-layer-edge parameters significantly change. The entropy layer gradually vanishes along the downstream direction, and the effects of chemical reactions are concentrated in the boundary layer. The entropy swallowing point of the equilibrium gas does not significantly differ from that of the perfect gas. For all the analyzed cases, chemical reactions stabilize the entropy layer instability modes. The instability region and the frequency range of the equilibrium gas decrease, and the growth rate of the most unstable perturbation of the equilibrium gas is considerably smaller than that of the perfect gas. Moreover, the results show that the equilibrium gas has a minor influence on the process of the blunt cone boundary layer solution tending to the sharp cone solution.

Symmetries of Calabi-Yau prepotentials with isomorphic flops

Calabi-Yau threefolds with infinitely many flops to isomorphic manifolds have an extended Kähler cone made up from an infinite number of individual Kähler cones. These cones are related by reflection symmetries across flop walls. We study the implications of this cone structure for mirror symmetry, by considering the instanton part of the prepotential in Calabi-Yau threefolds. We show that such isomorphic flops across facets of the Kähler cone boundary give rise to symmetry groups isomorphic to Coxeter groups. In the dual Mori cone, non-flopping curve classes that are identified under these groups have the same Gopakumar-Vafa invariants. This leads to instanton prepotentials invariant under Coxeter groups, which we make manifest by introducing appropriate invariant functions. For some cases, these functions can be expressed in terms of theta functions whose appearance can be linked to an elliptic fibration structure of the Calabi-Yau manifold.

Investigation of hypersonic cone boundary layer stability regulation with plasma actuation

Boundary layer transition has always been a frontier in the field of fluid mechanics, and hypersonic boundary layer stability experiments can help reveal the physical mechanisms behind such transitions. In particular, the regulation of unstable waves in boundary layers is critical for transition prediction and control. Plasma actuation is a popular flow control method that has made progress in moderating the stability of supersonic boundary layer. However, there have been few studies on regulating the stability of hypersonic boundary layers with plasma actuation. In this paper, wind tunnel experiments are carried out under Mach 6 flow to study the stability regulation of a hypersonic sharp cone boundary layer with nanosecond pulsed plasma actuation. First, the typical characteristic structure of the rope-like structure is captured by the high-speed schlieren method. Then, combining the sensor results and theoretical analysis, the rope-like structure and the dominant instability wave resolved by the schlieren power spectrum density method are determined to correspond to the second-mode wave. The characteristic unstable quasi-ordered structure of the boundary layer under actuation is then extracted, and the impact effect and modulation effect of this structure on the second-mode wave are analyzed. Finally, the mechanism by which actuation influences the boundary layer instability is studied using proper orthogonal decomposition. The results show that actuation can enhance boundary layer pulsation, and the coupling effect between the actuation and boundary layer can produce regular unstable quasi-ordered structures. The intrinsic mechanism works by impinging on and modulating the second-mode waves, and there are characteristic modes of the rope-like structure and the unstable structures distributed over the whole flow-direction range. This verifies the ability of plasma actuation to stimulate the instability of hypersonic cone boundary layers and provides technical support for the further development of transition control methods.

QCD anatomy of photon isolation

To separate the energetic photons produced in hard scattering processes from those from other sources, measurements impose isolation requirements which restrict the hadronic radiation inside a cone around the photon. In this paper, we perform a detailed factorization analysis of the QCD effects associated with photon isolation. We show that for small cone radius R, photon isolation effects can be captured by a fragmentation function describing the decay of a parton into a photon accompanied by hadronic radiation. We compute this fragmentation function for different isolation criteria and solve the associated renormalization group equations to resum logarithms of R. For small isolation energy, the cone fragmentation function factorizes further, into collinear functions describing energetic quarks and gluons near the cone boundary and functions encoding their soft radiation emitted into the cone. Based on this factorization we also resum the non-global logarithms of the ratio of the photon energy and the isolation energy, so that we control all logarithmically enhanced terms in the cross section. In this limit, we provide a simple formula to convert NNLO cross section results from smooth-cone isolation to fixed-cone isolation.

Electrically Induced Optical and Structural Response of Cholesteric and Nematic Droplets with Conical Boundary Conditions

The electro-optical response of polymer dispersed liquid crystals films has been studied. The polymer specifies the conical boundary conditions for the cholesteric and nematic LC. It is shown that for the cholesteric-based film with the relative chiral parameters of droplets equal to 0.32, control voltages are less than control voltages for the nematic-based film. The threshold voltages are 2.7 V and 4.9 V, and the saturation voltages are 7.3 V and 9.0 V for the cholesteric-based and nematic-based films, respectively. At saturation voltage, the light transmission of these films is over 80 %. The cholesteric-based film turns into a strong scattering state during 85 ms after switching off voltage, while the nematic-based film turns into initial scattering state during a few days. Significant differences in the electro-optical response of the studied films were explained using an examination of electrically induced transformations of the orientational structures formed in nematic and cholesteric droplets. Polymer dispersed cholesteric liquid crystals with conical boundary conditions are prospectful for the development of devices with low-voltage control.

Effect of Reynolds number on second-mode waves in transitional hypersonic boundary layers

The second-mode instability plays an important role in the natural transition of hypersonic boundary layer. In this paper, the Reynolds number effect on the second-mode waves has been experimentally investigated using the Nanoparticle-tracer based Planar Laser Scattering (NPLS) technique and PCB® fast response pressure sensors in Mach 6 quiet wind tunnel. The flow visualization results clearly capture the rope-like second-mode waves and the “quiet zone” before breakdown. The wavelength of second-mode waves is approximately twice the local boundary layer thickness, increasing with the streamwise distance and decreasing with the Reynolds number. The time delays between sensors indicate no significant Reynolds number effect on the propagation velocity of second-mode waves. The average velocity is about 0.82Ue. The characteristic frequencies are collated at different streamwise locations under different Reynolds numbers and show a linear proportion to Re/x. Based on the growth law of compressible conical boundary layer thickness, the characteristic frequency relation and wavelength relation are derived as a function of Reynolds number and streamwise distance. The theoretical estimation values agree well with the experimental results, which provides the potential feasibility to predict the characteristic frequency and wavelength in other tunnels.

Investigation on transition correlation of conical boundary layer in hypersonic wind tunnel experiments

The wind tunnel experiment is an important approach to studying boundary layer transition. In this study, the effects of bluntness, unit Reynolds number, and wall temperature ratio on hypersonic conical boundary layer transition were studied using numerical simulations and linear stability analyses based on the wind tunnel experimental data. Through the flow similarity principle, the treatment of the bluntness-varying problem was determined. Combining the experimental transition data and theoretical analysis results of sharp and blunt cones at home and abroad, the relation between the transition factor Ntr and the unit Reynolds number before ‘N factor reversal’, as well as the relation between the transition value Rtr and the unit Reynolds number from ‘N factor reversal’ to ‘transition reversal’ were determined too. Finally, according to the wind tunnel test data of China Aerodynamics Research and Development Center, the effect of wall temperature ratio on the receptivity of blunt-cone boundary layer was stated out, and the correlation of transition Reynolds number under different wall temperature ratios was determined. The influence law of parameters in this correlation was also determined.

Enhancing low velocity impact characteristics of glass fiber laminates by short fiber reinforcement—Failure evolution and damage mechanisms

AbstractFor enhancing impact characteristics, woven glass fiber epoxy laminates are reinforced with short fibers. The 6‐mm‐long slender fillers, when added up to 4% in the matrix, exhibit no influence on the flexural modulus, but at 2% they maximize the laminate's flexural strength. While the dissipation energy continues to increase up to 30 J of impact, the laminates' post‐impact load bearing capacity gets significantly affected beyond 20 J. The reinforced laminates exhibit better elastic response and enhanced damage resistance with as high as 50% reduction in the visible damage area as well as up to 35% increase in the damage initiation force. The degree of damage shows excellent correlation with the visible damage area. The distinct through thickness conical region, diverging from the impact site, is attributed to the presence of microcracks oriented along the fiber directions. The cone boundary, from where the interlaminar failure initiates, is largely the manifestation of transverse matrix cracks. While the damage cone with greater divergence indicates reduced impact resistance of the laminate, the orientation of transverse matrix cracks remains unaffected by the impact energy or the filler content. At low impact energies, the failure initiated from the fiber/matrix interfaces, coalesce to form the matrix cracks, which act as a precursor to the interlaminar failure. However, at high energy levels, several failure mechanisms simultaneously develop with no clear indication of the order of damage evolution. The short fibers enhance the laminate's impact resistance either by arresting the cracks or by developing tortuous crack path with high energy dissipation.

Birth and annihilation of topological defects on the nematic–isotropic interface during droplet coalescence

ABSTRACT In our work, we for the first time observed simultaneous birth and subsequent annihilation of two types of defects on nematic–isotropic interface: point boojums and localised equatorial defects. The investigations were made in the two-phase nematic–isotropic region in nematic droplets with conical boundary conditions. We found a new type of localized defects formed from equatorial ring defects in confined geometry of planar optical cells. During coalescence of nematic droplets, we observed formation of four antipodes of boojums and localised equatorial defects, followed by their pairwise annihilation with existing defects. The dynamics of defect annihilation was investigated.

Transitional flow structures in heated hypersonic boundary layers

Transition in a Mach 6 flared cone boundary layer over a heated wall has been investigated in the Mach 6 wind tunnel at Peking University using visualization, focused laser differential interferometry, infrared imaging, particle image velocimetry (PIV), and direct numerical simulation (DNS). The model's wall-temperature ratio η=Tw/T0 (where Tw and T0 are, respectively, the wall temperature and oncoming stream stagnation temperature) can be controlled to vary from 0.66 to 1.77. An ultrafast illumination image system has been used for Rayleigh-scattering visualization and PIV to experimentally capture the dynamics of the transition. Lagrangian flow structures are revealed by both the DNS results and the time-resolved PIV data. The effect of wall temperature on the transition is investigated, and it is found that increasing η initially delays but then promotes the transition to turbulence, with the reversal point being near η≈1. The turbulence onset mechanism over the heated wall for η=1.50, where first-mode-induced oblique breakdown dominates, is then investigated, and it is shown that lifting-up three-dimensional (3D) waves appear around the critical layer owing to the nonlinear development of the oblique first mode. Consequently, a downward sweep motion occurs to compensate for the lifting low-speed fluid, with the formation of a warped wave front. High-shear layers are created around the 3D Lagrangian waves and strengthened to cause the formation of a Λ-vortex. In general, this lifting-up 3D wavepacket has been confirmed to play a determining role in hypersonic turbulence production over a heated wall, which is similar to the findings in incompressible boundary layers.

An USBL/DR Integrated Underwater Localization Algorithm Considering Variations of Measurement Noise Covariance

Ultrashort baseline (USBL) positioning system is an important part of the integrated navigation for underwater vehicles. The single USBL positioning system has problems such as reduced accuracy of azimuth measurement due to target motion and large impact of small angular variations, especially in the region where the target is close to the conical boundary, that is, the low-elevation region. To improve the positioning accuracy of the USBL-based integrated navigation system, a tightly coupled USBL/Dead Reckoning (DR) integrated localization algorithm that considers the time varying characteristics of the measurement noise was proposed, and the filtering model of the algorithm was designed. The algorithm exploits the mechanism of the azimuth measurement covariance variation of the USBL system, constructs an adaptive measurement noise estimator for the USBL system, and applies it to the integration filtering of USBL/DR data. A nonlinear extended Kalman filtering (EKF) model was used to fuse the USBL positioning and dead reckoning trajectories. A number of simulation tests with different elevation angle settings were performed to compare the performance of the proposed algorithm with that of a conventional EKF for underwater localization. The test results reveal that the proposed algorithm can effectively reduce the positioning error caused by the change in the relative azimuth of the acoustic signal owing the motion of the mother ship and the motion of the underwater vehicle.

Liquid Crystal Materials under Conical Boundary Conditions

Liquid Crystal Materials under Conical Boundary Conditions

Light Cones as Quantum Phenomena

Quantum erasure experiments push the boundary between the quantum and classical worlds by letting delayed events influence the state of previously recorded and potentially widely distributed classical information. The only significant restriction to such unsettling violations of forward-only causality is that the distribution of forward-dependent information cannot cross out of the light cone boundaries of the event in the past, a feature that ensures no violations of causality — no rewriting of anyone else's recorded histories — can occur. The erasure interpretation of this conundrum requires rewriting of information recorded and distributed in the past, which would itself be a violation of causality. The quantum predestination interpretation removes the causal rewriting issue. However, quantum predestination requires detailed coordination of inputs from outside of the forward-dependent event's light cone, thus massively violating the same limit that prevents causality violations in such events. Yet another approach is to invoke the Schrödinger's cat variant of quantum erasure in which arbitrarily complex classical events within the light cone become quantum dependent upon the future event. As with all Schrödinger's cat interpretations of quantum mechanics, this variant of quantum erasure violates causality by discarding local classical histories such as the information-rich state of the cat's body. The most straightforward interpretation of erasure experiments is to follow the lead of the equations themselves, which transform on paper as if their components are independent of ordinary space and time limits, up to the limits imposed on them by the speed of light. Interpreting the light cone of each quantum system as an atemporal, aspatial unit in which classical time and space have no meaning results in a multi-scale, matter-dependent definition of spacetime in which every light cone is a singular quantum entity. In such a universe, both time and space are defined not as pre-existing, mass-independent continuums but as the consensus of vast numbers of constantly interacting and mutually limiting quantum-entity light cones.

Oblique light incidence method to study topological defects in nematic layers with conical boundary conditions

A polarization microscopy method to investigate the orientational structures and boojums formed in the chiral and achiral nematic layers under conical (tilted) boundary conditions has been developed. Oblique light incidence on nematic layer is used, due to which the phase difference between the ordinary and extraordinary waves depends on the director’s azimuthal angle. The phase difference gets maximal when the director azimuthal angle of achiral nematic varphi (x,y) = 0 and an azimuthal angle at the center of the chiral nematic layer varphi _0(x,y) = 0 independently of the total twist angle varphi _{TOTAL}. It has been found that the m=+1 boojums with the phase xi = pm 90^circ and xi = (-90^circ + varphi _{TOTAL}/2) are formed in achiral and chiral nematics, respectively, at the director tilt angle theta _{d/2} cong 40^circ at the interface. In addition, the defectless structure of chiral nematic with the periodically variable azimuthal director angle on the substrates has been studied.

An adaptive boundary element method for the transmission problem with hyperbolic metamaterials

In this work we present an adaptive boundary-integral equation method for computing the electromagnetic response of wave interactions in hyperbolic metamaterials. The indefiniteness of the permittivity tensor gives rise to preferential wave radiation within the propagating cone for the hyperbolic media, and this induces sharp transition for the solution of the integral equation across the cone boundary when waves start to decay or grow exponentially. In order to avoid a global refined mesh over the whole boundary, we employ a two-level a posteriori error estimator and an adaptive mesh refinement procedure to resolve the singularity locally for the solution of the integral equation. Such an adaptive procedure allows for the reduction of the number of the degrees of freedom significantly for the integral equation solver while achieving desired accuracy for the solution. In addition, to resolve the fast transition of the fundamental solution and its derivatives accurately across the propagation cone boundary, adaptive numerical quadrature rules are applied to evaluate the integrals for the stiffness matrices. Finally, to formulate the integral equations over the boundary we also derive the limits of layer potentials and their derivatives in the hyperbolic media when the target points approach the boundary.