Periodic Sidewall Research Articles

Temporal characteristics of hypersonic flows over a double wedge with Reynolds number

Laminar hypersonic flows at Mach 7.10 with unit Reynolds numbers of 5.2×104, 1.04×105, and 4.14×105 m−1 over a 30°/55° double-wedge configuration were studied to investigate the spatial–temporal characteristics of the flow in a time-accurate manner. Close comparisons were made between previous kinetic and current continuum approaches to test the validity of the continuum assumption, especially considering the presence of large gradients associated with shock–shock and shock–boundary layer interactions, as well as spanwise instabilities. Previous results from direct simulation Monte Carlo, which inherently predicts rarefied effects such as velocity slip and temperature jumps, were found to be in very close agreement with the current work, even for the lowest Reynolds number. The impact of velocity slip and temperature jumps on flow and surface parameters was investigated, and comparisons were made with a no-slip and constant temperature wall model. The temporal and spatial variation of two- and three-dimensional flows were thoroughly investigated using two-dimensional (2D), three-dimensional (3D) periodic sidewall boundary conditions, and a full 3D configuration consistent with existing experimental data. Close comparisons among the 2D and 3D cases were made. The characteristics of 2D periodic oscillations were reported for the moderate Reynolds number case for the first time. The presence of spanwise instabilities, even at a relatively low free stream pressure of about 100 Pa, establishes that the flow field depends on spanwise effects and is fully 3D. High-fidelity numerical schlieren videos captured strong spanwise oscillations for 3D configurations.

Large-eddy simulation of Rayleigh–Bénard convection at extreme Rayleigh numbers

We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh–Bénard convection (RBC) for Rayleigh numbers ranging from 106 to 1015 and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. [“Classical 1/3 scaling of convection holds up to Ra=1015,” Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (2020)] albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at Ra=1013, we use grids that are 1/120 times the grid resolution as that of the DNS [Iyer et al., “Classical 1/3 scaling of convection holds up to Ra=1015,” Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (2020)]. The Reynolds numbers in our simulations span 3 orders of magnitude from 1000 to 1 700 000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as Nu∼Ra0.321 and Re∼Ra0.495. We also perform LES of RBC with periodic side walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477, respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers and, hence, enable us to test the transition to the ultimate convection regime.

Flat-Top, Sharp-Edge Add-Drop Filters Using Complementary-Misalignment-Modulated Grating-Assisted Contradirectional Couplers

We demonstrate flat-top, sharp-edge, silicon add-drop filters using apodized grating-assisted contradirectional couplers (contra-DCs). Periodic sidewall corrugations are imposed on both sides of two asymmetric strip waveguides for contradirectional coupling between the first two TE supermodes of a two-waveguide system. Gaussian apodization is applied to suppress the sidelobes. By laterally shifting the positions of both waveguide Bragg gratings in a complementary manner, which is called complementary lateral-misalignment modulation, our devices avoid phase errors which impair the spectral responses for conventional lateral-misalignment modulated contra-DCs. We demonstrate a complementary lateral-misalignment modulated (CLMM) contra-DC that has a flat-top, rapid roll-off, drop-port spectral response with a sidelobe suppression ratio (SLSR) of 20 dB. We also demonstrate a series-cascaded CLMM contra-DCs that has a higher SLSR of 39 dB and a sharper filtering edge. ©

Localization of water surface waves in a heterostructure channel with corrugated sidewalls

This paper describes the fabrication of a water channel heterostructure by combining two types of periodic sidewalls with different duty ratios. This enables the manipulation and localization of water surface waves in bands that are traditionally inaccessible. It is well known that such forbidden bands can be created by the introduction of periodicity, in which the wave propagation is efficiently attenuated when the Bragg condition is satisfied. Through experiments and simulations, we show that an extraordinary transmission arises in the bandgap after two types of periodic channels are combined, even though they have similar forbidden bands. Waves that cannot travel along each channel then begin to propagate along the heterostructure channel. The measured surface amplitude of the water waves indicates that the localization around the interface of two periodic structures is responsible for the extraordinary transmission. The localized energy of water waves shifts according to the distance between the two periodic structures, and the localization and transmission disappear at certain distances. The measurement and analysis of this intriguing phenomenon of water wave manipulation will benefit applications in the collection and utilization of water wave energy.

3D outcrop modelling of large discordant breccia bodies in basinal carbonates of the Apulian margin, Italy

Large discordant breccia bodies (LDBBs) are important record keepers of the tectonic and gravitational evolution in platform-to-basinal settings, and have important implications for fluid-flow migration and compartmentalization of tight carbonate reservoirs. In the Gargano Promontory of southern Italy, LDBBs occur within a Cretaceous slope and basinal carbonate succession. We use field mapping and Unmanned Aerial Vehicle (UAV) -based Structure from Motion (SfM) Photogrammetry to document otherwise inaccessible cliff-side exposures of seismic-to subseismic-scale vertical discordant breccias. LDBBs are up to 50 m in width, more than 80 m in height and display internal chaotic or aligned clast fabrics. The formation which generally contains the LDBBs is characterized by beds of cherty pelagic limestone intercalated with calcarenites, calciturbidites and horizons of mass transport deposits. The mass-transport deposits can be correlated across the chaotic breccia bodies, indicating only slight or no vertical displacement across the adjacent walls. The bases of the breccia bodies are always hidden below current sea level, while the rarely exposed tops are capped by bedded intervals of the host rock formation. Timing and origin of the studied breccias were determined using several lines of evidence, such as stratigraphic provenance of clasts in breccias, mutual relationships of structural and sedimentologic features, and previous studies which establish that the age of dolomitizing cements in the LDBBs formed at different times and by different processes (fault shearing and solution collapse). This work investigates the size, shape and geometry of these breccia bodies whilst also providing cm-scale detail of the textural features in otherwise inaccessible outcrops. We suggest that breccias formed as a result of solution exploiting a pre-existing fracture network characterized by large-scale vertical strike-slip or oblique-slip faults. Initial displacement along these faults created a wide fault damage zone, where fluid migration was later focused to create a zone highly susceptible to solution and subsequent periodic sidewall collapse.

DEM analysis of passive failure state behind a rigid retaining wall: effect of boundary conditions

Discrete Element Modelling (DEM) is a virtual testing method that enables multiscale studies on granular materials. DEM provides a well-controlled testing environment, which enables precise systematic evaluation of the factors influencing the bulk response. The current study focuses on the behaviour of cohesionless backfills while a passive state of stress is simulated (i.e. rigid retaining wall translates toward backfill). Though particle-scale properties (e.g. size, shape and cohesion) play an important role on the macro response, the main objective in this study is to highlight the extent by which boundary conditions are important. Thus, identical dense packings are subject to the following boundary conditions: smooth/rough retaining wall and smooth/rough/periodic sidewalls (necessary for maintaining plain-strain conditions). Based on the DEM results, the failure surface geometries, wall pressure distribution and dilative response of the specimens are evaluated. It is seen that a curvilinear slip surface, similar to that observed in experiments, is only obtained once a rough retaining wall and periodic sidewalls are available. The overall observations suggest that the mobilisation of the passive state of stress, for a cohesionless granular assembly, is highly sensitive to the considered various boundary conditions.

Observation of water surface wave localization in a trough with periodic sidewalls

We demonstrate the localization of water surface waves and its evolution by introducing a defect into a trough with periodic sidewalls. Taking the advantage of water wave visualization, we observed a defect mode arising in the forbidden band and its formation process, that the water waves gradually accumulate at the defect, and accordingly, the energy gets smaller in the incidence part but larger in the exit part. After a certain time, when the accumulated energy gets large enough to produce a defect mode, we can obtain a steady state and an extraordinary transmission. It was also found that the transmission frequency linearly depends on the defect length with the negative slope and the localizations in different defects were also observed and analyzed. Due to the ubiquity of wave phenomena, the observation of water wave localization not only present a visual picture for the fundamental resonance concept, but also find applications in various fields, such as underwater acoustics, ultrasonics, electromagnetic waves, and optics.

DREM: Infinite etch selectivity and optimized scallop size distribution with conventional photoresists in an adapted multiplexed Bosch DRIE process

The quest to sculpture materials as small and deep as possible is an ongoing topic in micro- and nanofabrication. For this, the Bosch process has been widely used to achieve anisotropic silicon microstructures with high aspect ratio. Reactive ion etching (RIE) lag is a phenomenon in which etch rate depends on the opening areas of patterns, aspect ratio of the trenches and other geometrical factors. The lag not only gives a non-uniform distribution of scallop size, but it also sets a limit for the maximum achievable aspect ratio. The latter since the mask suffers from persistent erosion. While different kinds of hard masks have been suggested to ensure a longer total etch time, here we report a correctly tuned 3-steps Bosch process – called DREM (Deposit, Remove, Etch, Multistep) – without mask erosion. The erosion-free feature is independent of the type of mask. For example, an aspect ratio of more than 50 is achieved for trenches with 1μm linewidths, while no erosion is observed for 360nm thin standard photoresists. The mechanism behind this extraordinary infinite selectivity is mainly due to the depletion of C4F8 deposition species. Furthermore, a linear ramping of the etch step duration is performed to achieve a uniform distribution of scallop sizes along the etch profile. This outperforms the usual broad scallop size distribution when no parameter ramping is performed and improves the straightness of the etch profile considerably, in addition, it allows an easier way to control periodic sidewall shaping. e.g., a sausage-chain-like feature is demonstrated with an almost perfect periodicity.

Generation of dense granular deposits for porosity analysis: assessment and application of large-scale non-smooth granular dynamics

The knowledge of structural properties of granular materials such as porosity is highly important in many application-oriented and scientific fields. In this paper we present new results of computer-based packing simulations where we use the non-smooth granular dynamics (NSGD) method to simulate gravitational random dense packing of spherical particles with various particle size distributions and two types of depositional conditions. A bin packing scenario was used to compare simulation results to laboratory porosity measurements and to quantify the sensitivity of the NSGD regarding critical simulation parameters such as time step size. The results of the bin packing simulations agree well with laboratory measurements across all particle size distributions with all absolute errors below 1%. A large-scale packing scenario with periodic side walls was used to simulate the packing of up to 855,600 spherical particles with various particle size distributions (PSD). Simulation outcomes are used to quantify the effect of particle-domain-size ratio on the packing compaction. A simple correction model, based on the coordination number, is employed to compensate for this effect on the porosity and to determine the relationship between PSD and porosity. Promising accuracy and stability results paired with excellent computational performance recommend the application of NSGD for large-scale packing simulations, e.g. to further enhance the generation of representative granular deposits.

Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-Bénard convection.

The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10(8) and 10(11) the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra ≥ 10(10). Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.

Response of mantle heat flux to plate evolution

By analyzing convection characteristics and surface and basal heat flux we investigate the influence on mantle convection of finite thickness plates with dynamically determined velocities and mobile boundaries. Our 6 × 6 × 1 Cartesian geometry numerical model features periodic sidewall boundary conditions, a lower mantle that increases in viscosity and a Rayleigh number of 5 × 106 (based on the uniform viscosity upper mantle). A calculation with 9 plates and fixed plate boundaries is compared with a second calculation incorporating evolving plate boundaries. The number of plates in the latter case fluctuates between 6 and 9. We find that mean heat flux output decreases during periods characterized by the presence of larger plates and that evolving plate boundaries cause surface (and basal) heat flux output to vary much more than the heat flux observed with either fixed plate boundaries or a free‐slip surface.

Lagrangian studies in convective turbulence

We present high-resolution direct numerical simulations of turbulent three-dimensional Rayleigh-Bénard convection with a focus on the Lagrangian properties of the flow. The volume is a Cartesian slab with an aspect ratio of four bounded by free-slip planes at the top and bottom and with periodic side walls. The turbulence is inhomogeneous with respect to the vertical direction. This manifests in different lateral and vertical two-particle dispersion and in a dependence of the dispersion on the initial tracer position for short and intermediate times. Similar to homogeneous isotropic turbulence, the dispersion properties depend in addition to the initial pair separation and yield a short-range Richardson-like scaling regime of two-particle dispersion for initial separations close to the Kolmogorov dissipation length. The Richardson constant is about half the value of homogeneous isotropic turbulence. The multiparticle statistics is very close to the homogeneous isotropic case. Clusters of four Lagrangian tracers show a clear trend to form flat, almost coplanar, objects in the long-time limit and deviate from the Gaussian prediction. Significant efforts have been taken to resolve the statistics of the acceleration components up to order four correctly. We find that the vertical acceleration is less intermittent than the lateral one. The joint statistics of the vertical acceleration with the local convective and conductive heat flux suggests that rising and falling thermal plumes are not associated with the largest acceleration magnitudes. It turns out also that the Nusselt number which is calculated in the Lagrangian frame converges slowly in time to the standard Eulerian one.

Wind and boundary layers in Rayleigh-Bénard convection. I. Analysis and modeling

The aim of this paper is to contribute to the understanding of and to model the processes controlling the amplitude of the wind of Rayleigh-Bénard convection. We analyze results from direct simulation of an L/H=4 aspect-ratio domain with periodic sidewalls at Ra=(10(5), 10(6), 10(7), 10(8)) and at Pr=1 by decomposing independent realizations into wind and fluctuations. It is shown that, deep inside the thermal boundary layer, horizontal heat fluxes exceed the average vertical heat flux by a factor of 3 due to the interaction between the wind and the mean temperature field. These large horizontal heat fluxes are responsible for spatial temperature differences that drive the wind by creating pressure gradients. The wall fluxes and turbulent mixing in the bulk provide damping. Using the direct numerical simulation results to parametrize the unclosed terms, a simple model capturing the essential processes governing the wind structure is derived. The model consists of two coupled differential equations for wind velocity and temperature amplitude. The equations indicate that the formation of a wind structure is inevitable due to the positive feedback resulting from the interaction between the wind and temperature field. Furthermore, the wind velocity is largely determined by the turbulence in the bulk rather than by the wall-shear stress. The model reproduces the Ra dependence of wind Reynolds number and temperature amplitude.

Effect of sidewall boundary conditions on unsteady high speed cavity flow and acoustics

The effect of sidewall boundary conditions on the computed unsteady flow and sound pressure level is investigated in a transonic open cavity. The hybrid approach used for modeling turbulence combines a Reynolds averaged mode in the boundary layer, and a large eddy simulation mode in the massively separated flow region within the cavity to resolve the wide dynamic range involved. Computational results are presented for the instantaneous vorticity and for the sound pressure level spectra. Comparison of the results obtained using inviscid and periodic sidewall boundary conditions show the sensitivity of the computed SPL spectra and autocorrelation to the conditions enforced at the sidewalls. The computed SPL spectra are also compared with available experimental results, with LES computational results, and with prior investigations based on the same hybrid turbulence model without the wall function used in the current investigation. The comparisons show that the current results obtained using inviscid sidewall boundary conditions are closest to the experimental sound pressure level spectra and that agreement is achieved at considerable saving in required computational resources.

Modal spectrum of planar dielectric waveguides with quasi-periodic side walls

This work presents an in-depth theoretical analysis of a planar layered dielectric waveguide with periodic side walls. It is shown that, apart from the conventional guided modes for which most of their energy travels within the dielectric dense medium, this guide presents other modes whose energy mostly travels in the air regions inside the side walls or outside them. In particular, the mode with its energy traveling inside the side walls is a low-loss and weakly dispersive mode that could be of interest for practical applications. Moreover, it has been demonstrated that this mode can be strongly excited by a realistic source, which has been done by showing that this mode is the main part of the spectrum radiated by a dipole line located within the air region inside the side walls.

Spectral shift and Q change of circular and square-shaped optical microcavity modes due to periodic sidewall surface roughness

Radiation loss and resonant frequency shift due to sidewall surface roughness of circular and square high-contrast microcavities are estimated and compared by using a boundary integral equations method. An effect of various harmonic components of the contour perturbation on the Whispering-Gallery (WG) modes in the circular microdisk and WG-like modes in the square microcavity is demonstrated. In both cases, contour deformations that are matched to the mode field pattern cause the most significant frequency detuning and Q-factor change. Favorably mode-matched deformations have been found, enabling one to manipulate the Q-factors of the microcavity modes.

A three-dimensional, two-way, parabolic equation model for acoustic backscattering in a cylindrical coordinate system

A new PE model for solving three-dimensional, forward and backward sound propagation in a cylindrical coordinate system is presented. The model marches a wave field in the radial direction including the azimuthal diffraction effects, and solves for a backscattered field based on a three-dimensional, single scattering approach. A periodic sidewall boundary condition is applied for computations in a 360-degree sector, while an approximate sidewall boundary condition is used for calculation in a sector less than 360 degrees. These two sidewall boundary conditions are verified by the numerical results. The major drawback of using the cylindrical coordinate system, when the backscattering solution is valid within a limited area, is analyzed using a geometrical-optical interpretation. The model may be useful for studying three-dimensional backscattering phenomena comprising azimuthal diffraction effects.

Rayleigh number scaling in numerical convection

Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.